Im Looking to upgrade because this build is getting old 1+ years

i want to be able to play newer games without being restrained to 60fps or having to mess with the settings all the time.

Also it sometimes overheats even with an extra fan, so bigger case would be better

Something like this would be fine;
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Use the 2x140mm fans as intake and the 120mm in the rear as exhaust. Nice little cooler to reduce CPU temperatures. Since you have up to £700, you could do a lot more, but not really necessary.

You could upgrade the CPU to a Xeon E3-1231 V3 if you want hyperthreading. You could add more storage if you feel it's necessary. I'd probably upgrade the PSU as well, because your current PSU is not very good, but it will do the job, so again, it's not necessary. You could get a higher end GPU, GTX 1070 would be your best bet for a higher end GPU. You could also upgrade peripherals, if you wish. If you're running a standard 1080p panel, I'd maybe look at upgrading to an ultrawide or 1440p. In which case, a GTX 1070 wouldn't be a bad choice. If you're running 2560x1080, or 1920x1080, a GTX 1060 would be fine. You could get a higher end case if you want, Enthoo Pro or Enthoo EVOLV ATX would be a nice choice. Though, the P400 is already a huge upgrade over your current case and will be more than enough.

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