Every purchase is different, and your position and the seller’s position needs to be taken into consideration before this question can be answered accurately. If the seller has already vacated the property and you have already secured a mortgage, exchange of contracts and completion can happen relatively quickly.
However, if you need a mortgage and the seller is still in the property, the exchange of contracts normally takes between 4 and 6 weeks, the completion takes between 2 and 4 weeks. So in total you should expect up to 10 weeks to complete the purchase. Please note that in Scotland conclusion of missives normally takes between 6 and 8 weeks.