House buying - What should the solicitor do.?

Why would he ask that? They all have to do the same stuff, it might just be whether you want a solicitor to hold your hand. We had been through six separate transactions before I had a clue what a solicitor did!

A conveyancer will do the work cheaply but may not really communicate with you, if you want one to hold your hand then you might be better off paying more for a good solicitor and asking him who, out of his recommended (read those who will pay him a referral fee ) solicitors will do that for you.

Or ask friends if they have a recommendation themselves - they won't have a vested interest.

They will all do the same thing for you, the Law Society has a protocol to follow. You won't get more or less work from a solicitor, just more or less service.

They will carrry out searches and look them over for you. They're not qualified to interpret but they will highlight potential issues and point you in the right direction.
They will look over any HIP.
They will obtain the Title Deeds for the property, that the person that owns it is the same as the person selling it, and check over any covenants, easements etc. to make sure that the property is safe to buy from that perspective and advise you of any deviation from a straight freehold property.
If it is leasehold they will interpret the lease and ensure that it isn't 'defective'
They will check that there are no outstanding debts on the property and that if there are, that these will be cleared upon completion and confirm that the amount you are paying will cover those debts.
They will try to ensure that any guarantees & certificates are obtained.
They will read over the Sellers Property Information form and ask any pertinent questions arising from that.
They might have a stock list of additional queries that they ask of the vendor .
They will check the contract of sale to ensure it suits you.
They will act on behalf of your mortgage company for the same.
They will register your sale with the land registry and submit your stamp duty for you.
They will exchange contracts with the other solicitor, will ensure that the mortgage funds will be ready, when exchange occurs, for completion date.
They will draw down the mortgage funds and transfer these to your vendors when you complete.
If there are any issues then they will attempt to resolve them with the vendor's solicitors.

What they won't do is advise you on any aspect of the condition of the building.

It's all the same across the board. They will break down between the cost of their time and other disbursements so you can see what they quote for. Some might carry out different searches than others as standard but they are all available to you and they will all ususally be offered to you. It's pretty set cost for searches which they pass directly on to you so you won't find one solicitor much cheaper than others for things like searches and Land Registry fees, just the service that they offer.

You might find that very cheap firms (I've never seen it with anyone other that a conveyancing firm) will have the cost of dealing with a mortgage company as an added extra instead of included in the cost.

Some of the cheapo firms use clerical staff, acting under supervision of a solicitor. That doesn't help you much if you need advice, rather than bits of paper being passed around.