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For timber (assuming you want decent stuff) I'd recommend one of the following:
Moss & Co You'd have to go there to select and pick it up.
Surrey timber order online or pick up in person.
Timbersource order online.I'm quite a long way West of you and my workload means for the next month or two I'll hardly be in my workshop so it will be difficult for me to do this for you, if you were closer it would be easier. However these are meant to be amazing for the money and are more than capable of doing what you're after, also they're compact so fit well in a shed or garage.
SE1. Need to also source some wood if you have any ideas. Not a massive rush on the job, ideally in the next month or so. Just a project to busy myself when the kids are asleep