So what if he was working for the CIA?
The USA is one of the UK's closest allies. It's not as if they need to have sleeper agents in the UK to get US-centric policies in place.
A really controversial film would be if Lang was in the pay of the Saudis, or the Israelis, or the Chinese communist party, but I guess that might be too close to the truth for some real-life former Prime Ministers.
Tony Blair probably had a good laugh at this film and then went off to count his billions...