According to my little black book of pruning:

raspberries throw up new shoots called primocanes every year. They form flowers and fruit in the second year - after which they die.

Those old canes need to be taken out at the base to leave room for new primocanes to come through.

When the new canes come through - choose 8-10 shoots per clump - and take out the rest.

There are autumn-bearing raspberries and they are pruned differently.

If whoever planted them has strung wires then, for the autumn-fruiting plants, remove the growing tip of the strong-growing primocanes at about 60cm above the ground once they've gone past this point. That's at the height of the first wire up from the ground. This causes laterals to form and then fruit in autumn.

The canes which have been tipped are removed after harvesting.
The canes you didn't tip get left to fruit and produce their main summer crop the following year.

Or ignore that and hope that fruit sets at the tip of vigorous primocanes for autumn picking.

Basic raspberry poxes - full strength Bordeaux at green tip time and half strength at white bud time... prune out and burn or otherwise safely dispose of diseased canes.

Hope for about a kilo of fruit per bush if the kids and birds don't get there first.

Feed in early spring, early summer, and early autumn when the soil is moist. 800g of 15% potassic serpentine superphosphate (or equivalent) per 10m of row in late winter; and then up to 300g of urea or equivalent per 10m for the spring summer and autumn feeds.

If it's been a while since the plot was limed - dolomite. But no oftener than every two or three years.

Take out any straying suckers.

If your ground is light - generous side dressings of well-made compost will help with holding moisture that you need for good plump and tasty berries.

Happy feasting.

I reckon these are an autumn fruiting raspberry such as Autumn Bliss that fruit on late canes. It is very late for summer raspberries to be fruiting in October. They are more likely to have gone over by then. The canes go very dark brown in colour compared with the new canes and the leaves start to fall after fruit has formed.
Autumn Bliss has very light brown canes.
I cut down the Autumn Bliss old canes round about November times when all the fruit has been harvested. I cut them off as near to the ground as possible ensuring that I do not damage any of the new shoots that are developing. I think you will be lucky to get 8-10 shoots per plant. The most I get is around three or four but that might be because I am so bad at gardening. I tie these in during the winter onto a wire frame. I don�t "tip" either my autumn or summer raspberries because they form side shoots whether I like it or not. Why make things complicated when they are not.
Autumn raspberry varieties seem to be smaller than summer varieties. I have seen Autumn Bliss grown without any support at all, while summer varieties can grow 1.5 metres tall in a good year. I grow 'Glen Prosen', which has firm fruit in mid-summer. These have usually well finished cropping by September and I cut the old canes out in October. Once you can identify old and new canes you can easily prune them.

Here is a link that might be useful: Allotment Garden