I'm assuming that this is a Standard Visitor Visa.
No, you cannot make the trip alone with your current visa.
A letter from your mother doesn't help, because your visa conditions are set by the authority that issues the visa (in this case, that's the UK). Nobody else can remove those conditions.
UK visitor visas for people aged below 18 can be issued for travelling alone or for travelling with an adult. The application requirements are different and you can't convert the latter into the former.
The guidance on the linked page states that if you have a visa for travelling with an adult
you’ll be refused entry to the UK if you arrive in the UK without them.