I would recommend against it since even though you are mentioning that your address is a london address, some people might get confused by the number having no area prefix and wonder where it belongs to.
Also consider the use case where I might have just quickly glanced at the number above your email (on the contact us) page and if I was located in UK and I just saw the number without the prefix, I would get confused about whether its a local number or an international number since I have no address information to confirm it against.
Also consider the use case where someone accesses your site through a VPN which has its server in UK (they might be physically located somewhere else in the world) and your system assuming the IP being from UK has truncated the prefix, The user might not know he has to add +44 0 to dial your numbers.
I recommend looking at this question for additional inputs.