The issue is not entirely clear because the Singapore authorities don't divulge the criteria for allowing or denying additional visit visas.
Quite a few Southeast Asia countries (Thailand, Cambodia, Laos, and I think Vietnam) have a rule that you can spend a maximum of 90 days in the country every 180 days. I had an employee who was caught at the Bangkok airport with 93 days of visitation on her passport in a 180 day period. She was kept overnight and put on the first plane back to Singapore.
Singapore does not explicitly state this rule, but as SMS and others have noted, doing a visa run to Malaysia or Indonesia after staying for 90 days, only to return a day later hoping for another 90 days, is probably going to raise red flags.
OTOH, as a Brit, you're eligible for a frequent traveler visa.
(
https://www.ica.gov.sg/enteringanddeparting/visitor/ftp).
This means you can use the automated facilities with your foreign passport. Nowhere on this page is there any specified limit to the number of times you can enter Singapore nor the duration of each visit. Thus, if you've got the travel budget, you might consider frequent visits of shorter duration.
With respect to your same sex marriage: Nowhere in the dependents pass policies and provisions is there any mention that the couple must be hetero. The only provision is that you be able to provide a valid marriage license, and since the UK allows same sex marriage with the same rights and responsibilities as hetero marriage (ie, not a "civil union"), I'd probably try to get a DP before worrying about visas and visa runs. I recall at least one same sex couple from the UK posting on this board that they had successfully applied.
https://www.mom.gov.sg/passes-and-permi ... /key-facts
In the end, all of these rules are to prevent foreign labor from entering Singapore under the radar and working illegally without a permit.