Your mother's will should state who her executors will be. Whoever is named as executor needs to seek a grant of representation (='probate') in order to to distribute her estate. If she (wisely, in my opinion) named you and your brother as executors (as well as beneficiaries) then you don't need a solicitor as the probate application process is usually fairly straightforward. (You're still free to appoint a solicitor to help you if you feel you need it though). However if your mother named someone else (such as a solicitor) as executor, then only that person can apply for the grant.
Assuming that you're an executor, the information you need can be found by starting here:
https://www.gov.uk/wills-probate-inheritance/applying-for-a-grant-of-representation
The Probate Registry staff are extremely helpful and efficient when it comes to the necessary form-filling. Don't hesitate so seek their guidance! You can find the contact details for the relevant Probate Registry office here:
https://courttribunalfinder.service.gov.uk/search/
(Don't be put off by the reference to 'courts and tribunals'. The information you require really is there and, although you'll technically be dealing with a 'court', there are no stuffy formalities to worry about. For example, nobody will be bothered if you turn up to swear the oath in a T-shirt, jeans and flip-flops!).