If we are not moved to pity by the sight of hundreds of thousands of refugees pressing at Europe's borders in a desperate attempt to find some sort of hopeful future, we have hearts of stone.

Pity is not our only emotion, of course. Add bewilderment, alarm and apprehension.

However, there are enough tragic sights and stories out there for us to want to do something. We're Christians, after all; helping people is what we do.

The question is, what precisely? And as Christians, are we prepared let prayerful thinking about the situation override our instinctive responses?

Look at those images of exhausted families crossing frontiers with nothing but the clothes they stand up in, or being pulled from the sea with moments to spare, and the answer seems obvious: they need food and clothing. We have wardrobes full of stuff we don't need, so let's pack it up and send it.

The instinct to help is sound. The problem is that so many people have already given to this worthy cause that charities are already overwhelmed. An IRIN news report entitled Amateur Aid: The Limits of Good Intentions references CalAid, founded after donations came flooding in as the result of a Facebook post which was shared 65,000 times, Kos Kindness on the Greek island that has seen thousands of migrants arrive by boat, and similar organisations in Lesvos and Macedonia.

In Calais, though 90 per cent of the Jungle's residents are men, donors are bringing items for women and children. It now needs warehouse space to store everything. Secours Catholique Calais, a group of local pensioners, reports receiving stained suits, high heels and erotic lingerie. "It used to give us a laugh," volunteer Pascal Froehly told The Guardian. "But now we don't feel like laughing so much." In another twist, there's a market developing among migrants in donated goods: bottles of oil are reportedly being resold by people who have been given more than they need by well-meaning volunteers.

British Christian charity Seeking Sanctuary, which has been working with Secours Catholique for some years, has now said it can't accept new donations. Demonstrating commendable restraint, it says: "The situation is somewhat complicated by the numerous Facebook groups which have sprung up over the last few weeks, each trying to deliver goods to Calais as soon as possible."

Of course, some supplies of clothing and food are needed. Established aid groups are often quite well-placed to distribute them, though newer groups founded out of a warm-hearted desire to help often struggle – IRIN notes that no-one at CalAid has experience of logistics, distribution, camp management or fundraising. It quotes spokesman James Fisher, who says: "We could really use some technical help. We're just trying to figure it out."

The aid community has known about the problem of too much charity for years. In the aftermath of Hurricane Andrew in 1992, which devastated the South Florida coast, truckloads of used clothing arrived in the affected areas. Unable to find anywhere useful to unload them, the drivers ended up dumping them by the side of the road. Rain and sun transformed them into piles of rotting fabric which gave cleanup workers another headache.

According to the US Federal Emergency Management Agency (FEMA) used clothing is "rarely a useful item" to donate to disaster relief efforts. It has to be cleaned, sorted and distributed, and agencies rarely have the time and resources to do so. Often it just ends up in landfill.

Donated goods are often useless. Sometimes they're deadly.  The US has a Center for International Disaster Information, aimed at informing people about best practice in responding to emergencies. It's run by Juanita Rilling, who told a NPR interviewer about working as a disaster specialist trying to help hurricane victims in Honduras. "One morning I received a call from one of our logistic operators, and he explained to me that they had a cargo plane loaded with medical supplies that needed to land," says Rilling. But the tarmac was full, with piles of donations that no one had requested. The plane had to find somewhere else to go. "It ended up upending everyone's plans by about 48 hours, which is critical time in a disaster," Rilling recalled.

Money is usually far more useful than supplies. But money's cold. People really like to feel that they're giving something personal. So one idea is for charities to set up something like a wedding gift list using an online provider like Amazon, populated with things it really needs and can use. According to IRIN, Kos Kindness asks its supporters to buy items on Amazon, using the site's Wish List function to direct donors to appropriate items. Another group, called Help Calais, has followed suit.

Wanting to help people is a good thing. But there's no particular blueprint in the Bible for exactly how we're to help. Christians have no particular insight, as Christians, into how to support migrants and refugees in Europe. What we have are principles, like compassion, willingness to welcome strangers and willingness to make sacrifices for other people. We're also very used to taking hard looks into our own hearts, being honest about our motivations and our weaknesses.

So if we feel impelled to help migrants, we need to be honest about why we're doing it: not to make us feel good, but to make a real difference.

This might mean taking high-profile positions and calling for a mass movement aimed at influencing government policy or supporting existing charitable work, like Krish Kandiah's recent appeal. With its grounding in practical solutions for real problems, that's the kind of thing I could get behind.

It might mean – and for most of us it's far more likely to mean – an under-the-radar donation by cheque or by text, which doesn't make headlines but which still does good.

There's a recently-identified phenomenon known as "virtue signalling", which means holding and expressing an opinion about something because it makes you look like an admirable sort of person. But the point about virtue signalling is that it's divorced from reality. What matters is not that you have concrete answers or useful contributions to make, but what your opinions and actions say about you – whether they're sensible or not.

Christians ought to be immune from virtue signalling, because we believe in prayer.

Prayer, in the eyes of the secular world, is a a complete waste of time. If Christians use prayer as a substitute for action, then of course it is. But prayer as an expression of trust and hope in God, leaving in his hands what we can't do for ourselves, energises and enthuses us. Prayer keeps us honest. When we pray, we open our minds and hearts to God. We don't need to signal our virtues, because we know we haven't got any. We can focus on what needs to be done, rather than on how we feel about it.

There's nothing straightforward about the migrant crisis. We have no unique wisdom as Christians about how to fix it. But we can at least offer to see things clearly, free of the need to impress others or to ease our own consciences.

Follow @RevMarkWoods on Twitter.