We used the solicitor recommended by the estate agent when we bought our house (yes, I know ) on the understanding that the estate agents would chase them up for us, and the agent wouldn't be able to blame the solicitor for any delays.
It worked out pretty well as it goes, and if/when we move again I may well use the same guys again.
As for your mortgage, we used a mortgage broker last autumn when we re-mortgaged our house, however he ended up arranging a mortgage through my bank (Barclays) as that was about the best deal we could find.
We spent hours on 'tinterweb looking at different options, but could do no better than the mortgage guy...
My word of warning would be about surveys - we've had two now, on two different houses (inc a full structural on our current house) both of which quite frankly wern't worth a w**k.
Unless I was buying a listed building, or something complicated I would stick with the cheapest 'valuation' survey.
The full structural was riddled with caveats, get-out clauses and was ultimately pointless.
I'm sure there'll be a loads of honest surveyors on here within minutes insisting you'll die if you don't blow £££ on the full structural... but hey this is just my experience.