What British Influence Is There In Gibraltar?

A lot.

They still use the British pound as their money and speak English as well as Spanish. Every person I've asked wants to remain part of the UK and NOT be part of Spain (I'm not English so I don't think they were just telling me what they think I want to hear).

The older people still remember Spain under Franco and don't fully trust Spanish democracy but the younger people don't fear Spain but believe that Gibraltar enjoys benefits of being part of the UK that they will lose when (or if) they become just a part of Spain. Since you can see Africa across the straits on any clear day it will always be a special part of Europe and  since the start of the economic unification of much of Europe I always expect a shift towards Spain each time I visit but as I stated above without exception, in MY experience, They want to keep their ties to England.