The average time to complete the whole process depends on the chain. Some new builds need to be completed in 28 days, whereas some leasehold purchases can take up to 12 weeks.
Unless there are specific factors you should estimate 6 to 8 weeks for a standard freehold or 8 to 12 weeks for a leasehold, however these may vary faster or slower depending on the chain (remember your solicitor is only one part of the chain).