Taking 16 month old through London, any sling ideas?

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Title says it all really. My 16 month old (who is quite heavy) and I would like to go and visit my sister in Essex. I want to carry him across London as sister has a spare stroller and I think the tube would be easier with him in a sling. I don't have one, and if I'm going to invest or make one I'd like to try something that would also be suitable for newborn so I can use it with the next one. Can I make a sling? Someone gave me instructions for making a stretchy one but how would I make a woven one?

Also does anyone know of any sling shops near brighton?

Any ideas?

If you are able to do some basic sowing you can make a mei tai - I made this one. Works great with my 3 yo and my 10 week old (have been using since he was about 2 weeks)

Perfect, thanks. I am going to have a go at making a mei tei........