Like many of these questions, the answer is - it depends!
For the average property, it probably makes no real difference, there is every possibility that the solicitor you last used has moved on etc.,etc.,etc.
All of the relevant information should be with the Deeds ( held by your lender) anyway so unless there is something marginally or very unusual , then see as above. There is no need for files to be transferred.
Your best bet is to ask for recommendations from family and friends of solicitors they have used that they were happy with. Then phone them and ask for a fee quote. Once you have decided who you want to act for you, you can instruct them.
As regards taking up the Deeds from your lender, there are currently two schools of thought on this.
1. Wait until you have a serious offer on the house before requesting Deeds. Yes, it will take a few weeks BUT if the house languishes on the market for months on end, then the Deeds are not taking up space in the solicitors office ( I have limited space in my own office).
2. Take them up at the earliest possible opportunity to be ready to leap into action! I have just closed a sale with a very quick lead in time - much to all parties astonishment!. However, it was quite fortuitous, a lot of things fell into place and the purchasers were not "tyre kickers". And the Vendors were very realistic with the sale price.
mf