A Double Teaset

Question

In this riddle you are given hints to solve for two (or more) different words that have two (or more) homophones/homonyms, A.K.A teapots. These teapots also relate in some way. Your goal is to identify all of the teapots and how they relate. If you are still confused here is the last one done by @AHKieran and the previous one done by me (that is currently unsolved).

This teaset riddle is slightly different in that for the two words you have to find there are two teapots for each and both teapots relate, so there are two relations that must be found.

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For the first word, teapots there are two,
One being a U.K. name for a common baked food,
Other being outerwear, close to a sweater,
Do you remember it during cold weather?

Continuing to the second word and both of its meanings,
Onto the first, an item that requires some preening,
Layer this one around and around,
Down to the last teapot, to eat without slowing down

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Hopefully I've struck a proper balance with this one between being too easy or too difficult. Hints may be added if deemed necessary and as always, Good Luck!

Answer 1

It seems clear that QuantumTwinkie has the correct second word. I think the first is

JACKET.

First meaning:

short for "jacket potato" = "baked potato" (so called because it's cooked with its skin on).

Second meaning:

coat-like outer layer of clothing.

Relationships:

You could scarf down a jacket potato. Or you could go out in cold weather and wear a scarf and a jacket. (Both of these might help you keep warm...)

Answer 2

Maybe for the first one

Battenburg(sweater and cake)?

For the second one

Scarf

Continuing to the second word and both of its meanings, Onto the first, an item that requires some preening,

Your clothing scarf may get tangled.

Layer this one around and around,

Around you neck it goes.

Down to the last teapot, to eat without slowing down

Scarfing down food.