Ref Gomev, the restriction to 1.5mm cable for 13A plugs is due to the physical difficulties of fitting larger cables into the plug. It is obviously not an electrical issue.
Using 2.5mm cable on a home made extension lead maybe seen as a bit of over kill of course.
Purely because terminating 2.5mm round flex / cable conductors into a standard three pin domestic plug head, can be JUST a little bit tricky.
Not impossible, but just a bit of a squeeze

.
But 1.5mm cable has been proven to be effective for use on a "Granny" lead.
The cable can never be to large in cross section ( within reason of course ) but it certainly CAN be too small !.
Some of these "Wind Up" cheap reels you can buy from the cheapo shops or the DIY sheds, are alright to power your electric drill for a quick job alright, but many of these are using 0.75mm cross sectional flex.
Okay to power a small electrical appliance for a shorter time, but definitely not suitable for the job in hand here.
Terminating multi strand 2.5mm flex into a IP65 out door socket outlet, via a water proof gland first and then preferably using a boot ferule kit to crimp each conductor, before connecting them to the face plate maybe seen as good practice as well.
Do it right, or don't do it all.
Just go buy a suitable rated cable.
Make sure the socket outlet is weather proof, as you MAY want to use the extension away from the home.