Can I plug a fridge freezer into a short extension lead?

Get an extension lead rated for 13 A. You can get rubberised ones which are a bit tougher - you don't want to skimp on the price.

Make sure it has some provision for mounting it on the wall and do so (use screws that won't rust, like brass or zinc-galvanised). That way, if water gets into the garage (like on those days it rains sideways) it won't get to the extension sockets.

It would be best to make sure that there is no way for condensation on the lead to trickle into either end - the plug end will be ok as that hangs down with UK sockets installed the right way up. For the extension outlet end, you just need to leave the cord hanging downwards a bit.

You might want to label the plugs with sticky labels or a marker pen.

Or you might have a electrician mate down the pub who'll install an extra double socket for the price of the parts and a couple of beers :)

Yes it will be fine, as long as you keep within the current ratings of both the main socket and the extension. As the current draw of the lights is minimal this isn't going to be a problem. This is what extensions are made for, and there's nothing particularly special about a fridge/freezer. Obviously mount the extension where it will be secure and dry.
Be safe, but don't fuss!

It appears that you want the extension cord just to split the outlet in two- is that correct? If so, what you want is just a (heavy duty) splitter, with possibly an extension cord to the lights after it, since I assume that the freezer isn't going to be moving.

The correct solution, is to install a new receptacle for the lights. You can brach off the existing circuit to feed the new receptacle, but you'll have to use proper wiring methods and materials.

Almost certainly, the manufacturer's instructions for the fridge specifically say not to use an extension cord.

Assuming U.K. The ring main feeding the double socket would (should) have 2.5mm wiring, capable of carrying 30amps. The double socket itself would feed 13amp plugs (with max. 13amp fuses. A tumble drier on one socket could pull 12amps. Plugging the fridge/freezer into the other would pull substantially less - and certainly intermittently - they're not using electricity all the time.

Any proper bought extension cable is rated at 13amps. That's the plug (and fuse), wire and socket/s. No matter how long/short it is. There will be no proble using that extension for the fridge/freezer, as long as there's no chance it will be affected by damp or water ingress. Thus kept off the floor.

Other appliances can be plugged into the extension block, but it makes good sense that the tumble drier stays in its own dedicated socket, not plugged in to the extension block.

Every appliance should have a watts rating showing. Won't do any harm to understand how watts and amps are related.