My inflatable hot tub says “don’t use with an extension cord”… but can I?

Sadly they don't explain WHY not to use it with an extension cord. I wonder if it's to do with the risk of having such connections outside in the elements?

The cord it comes with is 7m long, and where we want to site it is 6m from our outhouse. I've drilled a 1ft long hole through the stone wall of the outhouse to thread the spa's cord through… But once in the OH the plug still ends up 3m away from the socket. Would it be considered ok to run a standard 13A indoors extension cord to bridge the gap?

The OH socket is grounded (I'm in the UK) and on an RCD-protected circuit, and the spa has an RCD in its cord (and another in the pump/heating unit, I think).

Maybe their concern is voltage drop in the thinner conductors of a typical extension cord. Maybe I can buy a "heavy duty" one which would be largely equivalent to wiring a new socket in?

Or do I need to just admit defeat and wire a new socket in?

Thanks