hi Vanna, I am in the process of buying/selling at the moment. I have been advised that it will take approximately 10-12 weeks to sell my flat (and buy my house) from the date of the 'memorandum of sale'.
this is basically a letter confirming in writing that you have accepted an offer on your property (and includes the price sold for). From this date, your buyers should then instruct their solicitor and mortgate advisor to proceed with searches and surveys on your property. If you are buying a property at the same time, then try and arrange to keep a similar schedule. Once all of the surveys and searches have been done, and (hopefully) the sale is proceeding, it should take only 8 weeks or so from that point until you complete on the property and hand over your keys / get the keys to the new place.
I would sugest that you get your property on the market first as it is quite slow at the moment (not many properties go on the market coming up to christmas so there is more demand for the few available). This means that you can hopefully get an offer on yours, then you are in a good position to buy a new place.
Good luck!