I would be extremely reticent about leaving a car parked in any street for 6 weeks. Aside from the potential impact on local residents, I would surprised if someone didn't report it as abandoned after that period of time. Do you really want a phone call in the middle of night from the police or a local council enquiring about why you've left it there?

Yes, you can do it, but in a area where parking is generally quite restricted/difficult for local residents it's a pretty anti-social thing to do. There shouldn't be consequences, but you could understand if there were.

You could consider one of the many websites where residents offer their driveways, and cater for both short and long-term parking. Somewhere in the vicinity of Heathrow would be under £300 for 6 weeks.

Edit: JustPark offers options around £150. There's also a monthly option which would give a bit more flexibility for only a few pounds more.