If there's a will, the first step should be to read it to check who's named as executor.
That person (or persons, if more than one executor is named) should then seek grant of probate. Many people use the services of a solicitor to seek probate but it's not normally necessary. If your mother took the unwise ( = expensive!) step of naming her solicitor as executor you'll have no choice in the matter. Otherwise (unless the will is very complex) it's fairly easy for anyone (who's confident with a bit of form-filling) to apply for the grant.
Nobody can touch your mother's estate until grant of probate has been obtained but you've done nothing wrong by taking money out of a joint account (since you'd have been able to do that anyway if your mother was still alive). Technically you should have told the bank about your mother's death before withdrawing the funds (and provided them with a copy of her death certificate) but you won't find yourself in trouble for failing to do so.
Probate registry staff are extremely helpful and will guide you (or whoever the executor is) through the process of applying for the grant. Contact details for your local office can be found here:
http://www.hmcourts-service.gov.uk/infoabout/c ivil/probate/registries.htm
There's also a telephone helpline:
http://www.hmcourts-service.gov.uk/infoabout/c ivil/probate/helpline.htm
Chris