Looking for a place in London from late March

Hi,
I am a hospital pharmacist relocating from York to London to start a new job at Imperial NHS in late March/early April. I will be working at 2 different sites so would ideally like somewhere that is within a reasonably easy commute to the Hammersmith and Paddington areas. I am open to either joining an existing group or clubbing together with 1 or 2 like minded people to find somewhere that works for everyone. My budget would be around £1000 but I can be flexible for the right place. I currently have a car as well so somewhere with a space or where permits are available would be great while I figure out what to do with it.

I'm originally from Ireland but I have been living in York for the last 2 years. I lived in Portsmouth for university for 4 years before that so I have lived in a lot of shared houses! I really value a relaxed and respectful space to unwind after a days work. I'm friendly and sociable but also happy to do my own thing. I like exploring new places, going to the gym and meeting up with friends but I'm not a massive party person and like a calmer home environment.

Thanks for reading!
Conor.