Hmm, so expect maybe £1500 to buy now, probably £3000 to trade up (buy + sell). So thats £4500 wiped out immediately. How many years are they talking? If we say 4, the house needs to rise in value by almost £100 a month to meet costs. But then there is maintenance and repair, there is building insurance rather than just contents, there are all manner of things that don't apply when you rent. I'd say double it, you'd need to gain £200/month so in 4 years that house needs to be worth nearly 10k more than it is now, to break even.
That is of course without factoring in the difference in cost between rental and buying. Depends what their rent is, and what the mortgage would be really. Not as safe a bet in my eyes. If we guess with a 150k house, it needs a 6.5% rise in 4 years. Not a lot, but we have just had some of the worst house price rises in history.