I would have thought that just about every garden centre (and Wilkinson's) would sell something - usually in packets and painted dark green.
They always used to sell them in Woolworth's
There's the more natural willow sticks which you would probably get in a smaller independent place.

Garden Centers do not sell pea 'sticks' but do sell green plastic netting for the same purpose. If you want actual sticks then you would need to find long prunings from shrubs or dead twiggy branches that have fallen from trees in the woods.

Yep, around here, pea sticks--twiggy branches to support dwarf garden and sweet peas, or some kinds of bush beans--are strictly do-it-yourself found objects. The netting sold in garden centers works just as well, and better for taller growing varieties, and is reusable, provided you are able to clean the old vines off of them sufficiently.

6-8 foot canes.
Netting can be used but you need to secure it to canes first.
So may as well just use canes.

I have occasionally seem pea sticks for sale but not in garden centres, more in small shops, and there aren't many of those around any more. i use prunings, eg dogwood and forsythia - not necessarily ideal and they do tend to take root and they aren't big enough for taller plants. Hazel is quite good too if there is a coppiced area near you. If you use willow make sure to peel the bottom inch or so or they will all grow!

When pruning shrubs I always save useful looking branches and twiggy sticks and any type do the trick. Small ones, big ones, they are natural and look better than canes, although I have used canes which came from my bamboo. Kerria Japonica have very tall straight stems if you know anyone who has this large shrub. Might not be tall enough for sweet peas though.

Using 8 canes construct a tepee from 6' or 8' canes set in a 12" circle with a margarine carton top with holes in to draw them together at the top. Use garden twine wound around and between the canes to allow your sweet peas to climb. I found that works well and no struggling to get rid of the vines in the netting and they last for several years. I used to store mine in the garage when the sweet peas died back, as leaving them in the ground will eventually rot them.If the canes rot at the bottom then shorten them and use as supports for something else.

Oops, igonore my useless suggestions - I was thinking peas not sweet peas!

I. M. E., anything that works for peas, works for sweet peas, even though they are different species.

But sweet peas are much taller unless they are Jet Set or Knee hi.

Well, I have had 'Oregon Sugar Pod' and 'Wando' get over 2 meters tall. I do know that 'Royal' Sweet Peas can get up to a meter taller, in good conditions.

My sweet peas grow up to 14 feet high.

But Scrumpy, you have magic fingers!

Not really, it's called layering.
Soon as they get near the top of 8 foot canes you untie them, lay them along the ground and tie them up against a cane 5 canes away. Gives them a new lease of life and off they go again.