Flat Mains Cable for Door and Window Jambs, etc.

Flat power extension cords are available for US 120VAC. These are not ubiquitous, but are not too difficult to source.

Internet search for “flat extension cord” yields many colors, lengths, plug and receptacle styles for 120VAC.

The abbreviation "FFC" which stands for flat flexible cable might also make a good search term if you are considering modifying an existing cord or rolling your own. With all due risks of course regarding codes, AHJ, etc.

I think I would just use the standard cable and block the window up so it's not being damaged, then put some foam weatherstripping in the gap to seal it.

If you decide to block the window up, as suggested, for security you can drill a hole slightly above where the upper/lower windows cross and insert a nail or screw. This will prevent the window from moving up any further.

UK plug, and 220v ac delivered outdoors.

A three core cable suggests that the lights are either 220v ac, halogen or similar and expensive to run.

Most modern light sets are LED and have a transformer to 24v dc or less, so the transformer should stay indoors and the two core low voltage cable feed out, which will be small enough to fit through between the sealing edges.

An alternative is to get an outside socket installed where the lights can be plugged in.

https://www.screwfix.com/c/electrical-lighting/outdoor-sockets/cat3360008

The examples above are easy for an electrician to install and will also be useful throughout the year for other power in the garden.

Like the original poster (Randall) said himself, not recommended ! As GM1964 said, it would make far more sense and safer to have a Waterproof Socket mounted externally. Then you have an external power source where you can use any form of electrical appliances, tools etc. in the driveway / garden.
I have an external power socket which has a lock on it so nobody can access it when I am not using it or away from home.
If you are capable, find a socket inside your house that is mounted on an outside wall, remove the socket and drill a 12mm hole from behind the socket to the outside.
Connect a suitable 3 core cable to your indoor socket and the other end to an outdoor socket. once cable is in place fill space around the cable with Silicone to seal it and stop cold air entering the house. Bingo job done,, if you are not capable yourself, check if any of your friends are electricians, or get an electrical company to come by. It's less than an hours work so should not be that expensive.
Eurolite Euroseal 13A 1 Gang Switched Socket Double Pole Lockable Impact case | eBay

Remember: All outside sockets(receptacles) must have GFIC protection, and a cover that protects the socket from outside weather even when a cord is connected to it.

This can be done using a GFCI circuit breaker, or a GFCI socket. A GFCI socket inside can be the feed through type that will protect any socket down stream, but the sockets must be labeled as such.(Per NEC).

To be electrically safe, the in-house power source should be coming directly from a GFI equipped electrical outlet like those found in the bathroom or kitchen..

Christmas lights having a very low power drain an alternate power source can also be taken from a low leakage isolation or induction type of transformer.

Hi Randall, see if your kitchen has a suitable plug to an outside wall, that would then give you a F1 Switch protected circuit. Because most Kitchens are located at the rear of the house in the UK you would then need to run a suitable extension cord to the front of your house to power your xmas lights garden tools etc.
An alternative would be to see where your Switchboard is located and maybe run an link direct from there using the Kitchen or Bathroom F1 terminals.

Thanks everyone for your suggestions: I do have a pair of sockets which I installed at the back of the house, and, at Xmas I normally just run an extension lead to the front of the house. The design of the sockets was useless and the switches on both sockets have tiny bits of plastic which melted during very heavy prolonged loads. I will get round to replacing them soon. I just wanted a quick solution for last Xmas, and It seemed to me that a wide flat mains cable would be useful in lots of situation.

Well at least you're going to replace the proper sockets eventually, probably when you get a withit and find your aroundtoit !!

I've got one:-

But it doesn't seem to help!

Ah you only have a Roundtuit, you are missing the "Wiffit" , you have to have both together before they work.

use in a sentence to clarify

Hi, a Roundtuit and ein Wiffet are old english expressions for not doing something straightaway...
Its a way of delaying doing something by saying I'll do it when I get "around to it" or when you find time / energy / interest to do something... when I get with it wiffet.
Next time when your wife asks you to do something you can now confuse her by simply answering by saying you will do it when you get "aroundtuit" !

Followed by a swift smack upside the head.

Could it be that "Aroundtuit's" has led to an increase in domestic violence ??

I hate to sound like the code police, but it does look like a house fire ready to start if someone closes the window....

Maybe you need a piece of wood that would cover the opening of the window, with holes for the wires to run through. It would block the cold draft and protect the wires.

It looks as though the installation of a suitably protected outdoor socket is overdue. Consult a qualified local Electrician.

See post #10