No need for Planning Permission, technically though you would need Building Regs Approval though as, unless your garage is humongous which apparently it is not, you'll be digging down into earth that is currently supporting the garage/house wall foundations and undermining them. There is also waterproofing to think about, not forgetting the practicalities/safety aspects in terms of exhaust gasses, escape in the event of a fire etc etc.
Warning: Dig a dirty great 6ft deep hole in your garage floor without employing the services of a structural engineer at your peril.
The escape of exhaust gases is something to consider seriously.
Also the potential for the collection of explosive gases in the pit is worthy of consideration.
Don't forget that some gases are heavier than air so would not normally escape form a pit. Simply bending down into the pit atmosphere for more than a few seconds could be enough to cause unconciousness or even worse, poisoning.
Electrics in the pit require some serous consideration, not just the installation but also the tools in use.
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