Waterproof and fleece-lined handlebar pogies/covers (like the deliveroo moped style) are amazing, and you pretty much don't need gloves inside them. Occasionally I wear a thin pair if it's extra cold. I've got flat bars but I think you can get them for drops/hoods as well.
I've got some cheapo Ali Express ones that I'm not going to use if you fancy? Free if you can collect from SE20 or just pay for postage. I've got the flat bar version as well for work and they're pretty decent.
Waterproof and fleece-lined handlebar pogies/covers (like the deliveroo moped style) are amazing, and you pretty much don't need gloves inside them. Occasionally I wear a thin pair if it's extra cold. I've got flat bars but I think you can get them for drops/hoods as well.