If it was my property I'd remove those 6 smaller pavers from the footpath and dig down to the existing pipework, if it's at the correct depth then I'd run my new mdpe pipework in and leave enough spare to reach the meter.
If it isn't then I'd contact Thames water and tell them there original install isn't at the correct depth and ask if they are happy for the new pipe to be laid at whatever depth it is.
Get the new pipework ran to wherever you want your new internal stopcock and tell Thames water your ready to go, also tell them their external valve doesn't switch off completely and ask them to replace it at the same time.
They'll then likely tell you that as you haven't used an approved plumber if there is an issue preventing them completing their works when they arrive you'll be billed for the callout, provided you've used the correct pipe at the correct depth and your new internal stopcock is ready to go there shouldn't be an issue and the tw guy will just connect the mdpe up, they may refit the paving for you or not.
Just make sure you cover the hole and clearly indicate part of the pavement has been lifted and your unlikely to have any issues from the council unless your neighbours really don't like you and make a fuss, it should only be open 2 days if you can get a date from tw for their part