Famous, Rich and Homeless, BBC1James May at the Edge of Space, BBC4

A cardboard box? You were lucky ...

Hang on a minute, this can't be right – we're barely past the opening credits of Famous, Rich and Homeless, and Annabel Croft, the former tennis player, is crying already.

The other celebrities abandoning their homes for 10 chilly days and nights on the streets of London and Glasgow get a bit weepy at points. But at least ex-newspaper editor Rosie Boycott, comedian Hardeep Singh Kohli, the Marquess of Blandford – Charles James Spencer-Churchill, known as Jamie Blandford – and ex-Corrie actor Bruce Jones waited until they had their fair share of homeless treats before they gave the producers of this two-part reality documentary what they wanted to see. Poor Annabel, though, turned on the taps about 30 seconds after she waved goodbye to her perfectly home-baked family.

Maybe the more houses you have, the harder it is to leave them: all told, Croft and her newly homeless chums have 10 between them – and a palace (Blenheim).

The aim, I guess, of Famous, Rich and Homeless was to publicise the reality of living on the street. Unwisely perhaps, the programme opted for the boot-camp approach, and there was quite a bit of this lumpy "concept" to chew through before it came up with much to digest. Large dollops of the two programmes were taken up with the very stern John Bird, who set up The Big Issue, and Craig Last, an only slightly less stern man who used to work for a charity for the homeless, hauling the celebs to and from an anonymous warehouse where Bird and Last barked variations of: "If you thought that was horrible, wait til you see what we've got for you next!"

So, over the course of 10 days, each participant progressed from being dumped in central London to fend for themselves with no money, to spending a few days in the company of a long-term homeless "buddy", to, finally, crashing in a hostel.

There were touching moments: when Singh Kohli's homeless buddy, Sean, pointed out that the comedian shouldn't mind being woken up after midnight by a drunk woman offering them cigarettes – at least, he said, someone cared enough to check if they were OK. And who could fail to be moved by Mark, for whom a spiral of homelessness and heroin addiction meant he rarely saw his daughter. But these glimpses of the truth, succinct and grim, were few. The programme seemed less interested in the endless grind of homelessness itself than in the jittery emotional responses of media folk slumming it for a few days.

Boycott, the good liberal, gave up the £40 she felt she had "conned" out of a well-meaning young woman she begged from; Singh Kohli maintained a cast-iron good humour that only began to crumble in sight of the finishing line; Jones spoke almost entirely in tabloid pull-quotes ("I've seen things I thought I'd never see in my life!"); Croft, in a performance that made Julie Andrews look like a child-killing, crack-dealing witch, attempted to reform her new homeless chums by smiling at them very, very nervously; Blandford the ex-cokehead, with true druggie cunning, finagled his way into a five-star hotel for two nights before walking off the programme.

Weirdly, though, Bird didn't lose his temper at Blandford, but at the "fucking irritating" Croft for what he called her Florence Nightingale act. But Bird wasn't given much of a platform to explain his outburst as the programme hustled its participants towards its conclusion: that homelessness begins with a home that, for any one of countless different reasons, you're forced to leave. "If he thinks this is a game, it's not," was said of Blandford at one point – but perhaps the marquess knew this programme better than it knew itself.

How many homeless people could you permanently house with the money used to send a Top Gear presenter to the edge of space? Several people-movers'-full no doubt. But faced with the awesome heroics of space travel, I'm afraid I go all starry eyed. Last Sunday, with James May at the Edge of Space, the BBC chose to launch its season to commemorate the moon landings by putting May in the passenger seat of a U2 spyplane.

I quite like his Eeyore-ish contributions on Top Gear. But the higher May soared, the more impassive he became, until, at 70,000ft, with the curve of the planet falling away beneath him, and only a handful of humans further from Earth than he, he looked up through the visor on his helmet, raised his eyebrow and muttered: "Just noticed how dark the sky is ...".

James May: the most diffident man in the cosmos.