Yes, but all other lotteries are basically illegal, as MarcusF said, unless they are little things like church tombolas or something organised for your company’s Christmas party. Or the National Lottery, which is a special case.
It looks like the people running this “sell my house” lottery have consulted a lawyer and made sure that it is a game of skill, because the question that you are required to answer is not trivial (well, not unless you have access to Google and maybe 10 seconds of spare time. I don’t know if the UK Gaming Act has quite got its head round Google yet, though).
Anyway, I think what the OP may have been more interested in is, is this a legitimate way of dodging Stamp Duty (the tax levied on the purchase of a house, for the non-Brits still reading this, both of them).