Cooker wont fit due plug socket on wall so needs re-wiring

I've just successfully installed a new hob, and thought the single electric oven was going to be easy but hit major problems. The picture below shows whats on the wall looks like in my oven housing. Looks a bit like it was installed by cowboys to start off with. On the left is the wiring to the hob. On the right is a socket that is mounted to take a plug with 13A fuse that powered the last oven. New oven is same rating so thought I could just plug new one in and be away. Not sure it needs the plug with fuse but put it on and thought it was going to be that easy.
The problem is that the new oven is deeper and wont fit whilst the socket and plug are wall mounted. After the plaster I have only about 2cm to play with before where the back of the oven needs to be.

Now I am a complete Novice and probably shouldnt have even wired in the hob, with all these new regulations, so go easy on any advice. It will really need to be written for a complete bigger.
Should I just call in an electrician and pay the bill or can it be fixed easily. Can I wire the oven straight into the wires that go into the socket and thereby lose the additional fuse protection in the plug. If so, how??, or do I need to get the socket moved to where there is space.

Thanks for any help!!!

The best way to do this (and it will be ok because this is all hidden behind the cupboards) is to chase that supply cable back to behind an adjacent cupboard, and fit the socket here.

Alternatively, does the oven fit with just the socket and back plate there? If so, you could fit an unswitched FCU there with a flex outlet at the bottom. This works the same way as a plug with a fuse, but you cant move what you plug into them! And crucially, they take up less space than a plug / socket.
they look like this by the way!

And to alay any concerns, theres nothing wrong with wiring the socket like this. In fact, ours is wired this way. Though this looks as though it was done by the kitchen fitters . . .

Thanks for the quick response. Yes the cooker does just fit with the socket alone, and it is quite a deep socket, so a slightly thinner example that doesnt need a plug and has a built in fuse sounds perfect. I'll be back at homebase tomorrow for a look, and will update on my success. Thanks again for the response, it really is appreciated!!

Crafty. Just to let you know, your advice paid off and the cooker is now fitted and working. Thanks again. Pic below shows my superb handy work on the right.

nice one! always nice to know how people get on following our advice!

by the way, it would have looked much better if you changed that manky old cooker connection plate on the left! still, nobody's going to see it are they