You won't have a problem with the VWP rules you cited -- however, you may have another serious problem, see below.

The key words you cited are "as long as the trip does not terminate in contiguous territory or an adjacent island". This is because the 90 days allowed under VWP may include any time you spend in continguous territories or adjacent islands after entering the US.

Allowed under VWP (what you asked about): UK to Mexico, Mexico to US, US back to Mexico, Mexico back to UK, all within 90 days and all tickets in hand.

Disallowed: UK to US, stay for 40 days, US to Mexico, stay in Mexico for 40 days, return to US and stay another 11 days. Disallowed because you would stay in the US past 90 days from the initial US entry.

Gray area: UK to US, stay for 40 days, US to Mexico, stay for 6 months. Gray area because it is unclear whether staying in Mexico for 6 months counts as terminating the trip there. Probably still acceptable as long as you already have tickets out of Mexico and can clearly explain your plans.

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However, you mentioned "to see my fiancee". This can be a serious problem because US law implies that entering the US to see one's fiancee should be done with a K-1 fiancee visa. (The K-1 fiancee visa assumes you will get married in the US and subsequently become a permanent resident. It is a lengthy process to say the least.) If you want to see your fiancee but not get married on that trip, US immigration law does not really have an option for that. Depending on how much you can tolerate the risk of serious US immigration problems (ie, how much do your future plans depend on US immigration), you might not want to seek entry under VWP for this purpose.

Your plans are fine under the VWP rules you mentioned. See below for issues about going to visit a fiancee.

The key phrase you cited is "as long as the trip does not terminate in contiguous territory or an adjacent island". This is because the 90 days allowed under VWP may include any time you spend in continguous territories or adjacent islands after entering the US.

Allowed under VWP (what you asked about): UK to Mexico, Mexico to US, US back to Mexico, Mexico back to UK, all within 90 days and all tickets in hand.

Disallowed: UK to US, stay for 40 days, US to Mexico, stay in Mexico for 40 days, return to US and stay another 11 days. Disallowed because you would stay in the US past 90 days from the initial US entry.

Gray area: UK to US, stay for 40 days, US to Mexico, stay for 6 months. Gray area because it is unclear whether staying in Mexico for 6 months counts as terminating the trip there. Probably still acceptable as long as you already have tickets out of Mexico and can clearly explain your plans.

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You also mentioned "to see my fiancee". This can be a potential problem because some US officials (incorrectly) think that entering the US to see one's fiancee should only be done with a K-1 fiancee visa. Under 9 FAM 402.2-4(B)(1) you should be able to get a tourist visa to visit your fiancee temporarily, which implies that it should also be possible to do so under VWP. Here are some more resources about this issue: 1, 2, 3.