See Be’er Hetev, i dont have it in from of me now. He says that the Maharil assered, but the the Mahari Veil is mattir. But if the minhag in your place is to shave, then you should and there is no mokom to be machmir.
As far as i know, the minhag in London (and everywhere else that i have lived) is to shave for Shabbos erev lag ba’omer.