As it takes time to have a suit made to order, and SW had presumably looked in more than one shop in those pre-internet days, their wedding was obviously pre-planned. The (condensed) account I copied from TWS doesn’t suggest they eloped on a whim, and I don’t recall any other mention of the wedding, but several mentions of how her parents hated her dating Moth (“You’ll regret this, my girl, you’ll regret this until the day you die”; “He’s no use to you, he’s useless, pointless”), so she was seeing him behind their backs.
In TWS she writes:
”We’d sat on the mounded oak roots in the Park as my stomach churned and I tried to breathe, in the moments before we walked down to the house and unfolded the marriage certificate on the kitchen table”.
Earlier in the chapter she quotes her mother saying, “Moving in without getting married, that’s disgusting, you’re an embarrassment”. So they didn’t move in together: “I couldn’t take the final step of defiance”.
They weren’t such unusual sentiments, even as recently as the 1980s. It’s quite plausible that her mother demanded a local wedding reception to avert her own embarrassment at her wayward daughter.
Photos shown during the TV documentary showed a wedding cake, as well as the “family photo” where SW looks tense, Moth looks smug, and her mother looks to be over-acting the happy MOTB!