Are these intended activities legal to do in the USA under the VWP?

Yes, all this is fine. Some people have been denied entry to the US when coming to the US even temporarily to marry a US citizen, so you will see advice online (even sometimes from immigration lawyers) saying that you need a fiancee visa for this purpose. But the State Department's Foreign Affairs Manual says that a B-2 visa is appropriate for this purpose:

9 FAM 402.2-4(B)(1) (U) Fiancé(e) of U.S. Citizens or Permanent Resident Aliens

(CT:VISA-778; 05-13-2019)

(U) An alien proceeding to the United States to marry a U.S. citizen petitioner within 90 days of admission is classifiable as a K-1 nonimmigrant under INA 101(a)(15)(K). (See 22 CFR 41.81.) The fiancé(e) of a U.S. citizen or lawful permanent resident (LPR) may, however, be classified as a B-2 visitor if you are satisfied that the fiancé(e) intends to return to a residence abroad soon after the marriage. A B-2 visa may also be issued to an alien coming to the United States:

• (U) Simply to meet the family of his or her fiancé;

• (U) To become engaged;

• (U) To make arrangements for the wedding; or

• (U) To renew a relationship with the prospective spouse.

None of this mentions the Visa Waiver Program, but the VWP is explicitly applicable to travelers who would otherwise be admissible as B visitors. At 8 USC 1187(a)(1), the requirement is stated thus:

(a) Establishment of program The Secretary of Homeland Security and the Secretary of State are authorized to establish a program ... under which the requirement [to have a visa] may be waived ... in the case of an alien who meets the following requirements:

(1) Seeking entry as tourist for 90 days or less

The alien is applying for admission during the program as a nonimmigrant visitor (described in section 1101(a)(15)(B) of this title) for a period not exceeding 90 days.

...

The FAM is a document of the Department of State, but the Customs and Border Protection Inspector's Field Manual agrees in section "(2) Classification: B-2 Visitor for pleasure" (page 50):

Special notes:

...

(B) Determining eligibility. If otherwise admissible, admit the following as B-2:

...

(10) An alien coming to marry a U.S. citizen or lawful permanent resident with the intent to return to a residence abroad soon after the marriage;

The section on the VWP notes that it applies to "visitors for business or pleasure" on pages 115 and 116.

To overcome a possible skeptical immigration officer at the border, you can bring evidence of your intention to return to the UK, as well as evidence of your fiancee's plans to move there after marrying you. But I would not offer this evidence before it becomes apparent that the immigration officer is questioning your intention to leave the US.

When traveling under the VWP, the activities planned must be permitted under B visa.

VISITOR VISAS BUSINESS AND PLEASURE Overview

You are allowed to visit the USA for the reasons you outlined (i.e. marriage) under the VWP program. Unlike the UK which requires a marriage visa for the purpose of marrying, the USA does not have a visa type for that purpose.

Regarding your plan to come back to the US later in the year to get married: Did you already file the paperwork for your K1 visa? If so, that could raise some warning flags when trying to enter the country. Having a return ticket and other proof of ties to the UK (current lease agreement, job, ...) might be useful. If you haven't filed the paperwork, getting married this year is a very aggressive timeline. Even if everything goes perfect, you're probably still looking for January or February to be able to enter the US for getting married - March or April is probably more likely.

There is probably a reason why you want to get married in the US before moving to the UK, but getting married in the UK should be the simpler way.