this is how my house buying experience worked here. my was chain free (i didn't have a house to sell, and the house i was buying was empty so those owners didn't have to buy another place).
mid-aug--- put in offer for house
couple of days later--- offer accepted
month of september--- searches, approved for mortgage, mortgage company arranged survey, etc
sep 29--- signed contract. called exchange as its the day you actually exchange contracts and things start getting binding
oct 4--- completion day- day i moved in
now, i had a relatively smooth 6 week offer to move in timeline. but the housing market in the uk can be crazy for some. from what little experience i have in the US market, one of the big differences is that until you exchange contracts either side can pull out. even after spending ££££ on surveys, etc, the seller can take a higher offer, decide not to move, not find a house for them to move into, etc... and then you're back to square one.
my estate agent told me that 40% of house offers that are accepted don't make it to exchange/completion.
also- the above "rules" are for england. scotland has a different system of offers over, and binding offers, etc...
i 110% agree with texasex's suggestion. get a book that details how the house buying process is in the uk. well worth every penny! good luck.