Depends on the price range in which you're planning to buy and sell. We've just done it, and the costs are, frankly, eyewatering. Not going to quote figures cos I'll get jumped on, but you need to work on the basis of:
4% stamp duty on your purchase if over £500k;
2% or so of sale price in estate agents fee;
The above two are the biggies, and for a 4-bed house in London can easily add up to an extra £30K or more. Yes, you can get cheaper estate agents, but if the expensive ones sell your house aggressively, you may still end up better off than choosing a more laid-back cheaper one.
Also:
£2000 in solicitors costs (sale and purchase);
£1500 in removal costs (good removers, 5-bed house);
You can economise on these, but to an extent you get what you pay for. Cheap solicitors likely to be significantly less good ime. Ditto removers. Also remember:
Fee for mortgage application if applicable;
Spare money for replacing appliances if necessary;
Cost of redecorating if necessary;
Cost of changing locks;
May need to upgrade insurance.