Companies House only shows the company listed at their Lambeth address since 1984, although the company origin is 5 years earlier in 1979, so it is possible.

Curiously, despite being a mile away on the opposite side of the river, the location shots for Oscar nominated 1949 Ealing Comedy 'Passport to Pimlico' were mostly shot just south of the Lambeth road in the area around Hercules Street. According to the company's website, the Pimlico Plumbers London depot did feature in the film.

So even if they didn't trade in Pimlico before 1984, their depot is famous for being in a film about Pimlico!!