It is your responsibility to arrange your mortgage (not your conveyancer). But, it is very obviously an important part of the conveyancing process as, unless you are a cash buyer, it must be in place by the time your want to exchange contracts.
You can apply for a mortgage directly with lenders, or alternatively, you can use a mortgage broker who will do a lot of the leg work for you finding the mortgage deal that is right for you. There are various types of mortgages.
Although it is your responsibility to find apply for and secure your mortgage, your solicitor has 2 responsibilities to deal with in relation to your mortgage. The first is to ‘certify the title’ to your lender. This is simply confirming to your mortgage lender that they have completed the normal legal checks, and the legal title is as it should be. Your lender can sue your solicitor if they get this wrong!
Secondly, your conveyancer will provide you as the buyer with a ‘mortgage report‘ which will summarise any legal terms and conditions of the mortgage. Your conveyancing solicitor will NOT advise you on any aspect of the mortgage in terms of its suitability as a financial product for you.