I would agree - don't go for stinking as a first approach, but do go for official/formal (who have you raised it with before?)
You might want to reference the Department For Education Guidance here which doesn't specifically say anything about the skirts/trousers question but does give some principles that you can tie your argument to, to give it greater weight.
e.g.
"The DFE Guidance states that a school uniform plays a valuable role in contributing to the ethos of a school and setting an appropriate tone. It strongly encourages schools to have a uniform as it can instil pride; support positive behaviour and discipline; encourage identity with, and support for, school ethos; ensure pupils of all races and backgrounds feel welcome; protect children from social pressures to dress in a particular way; and nurture cohesion and promote good relations between different groups of pupils. Above all, many schools believe that school uniform supports effective teaching and learning."
In these kinds of cases of institutional inertia the trick is to make your approach appear absolutely reasonable, simple and low-risk for governors who have a hundred different things to think about and just want a quiet life.
I would emphasise the practical aspect for active play, and say that allowing girls to wear trousers (and also school uniform style shorts in the summer) would not undermine any of the DFE's aims, and would support some of them - ensuring pupils of all races and backgrounds feel welcome, supporting cohesion, and supporting a school ethos which (hopefully) does not impose arbitrary expectations about girls and boys.
You could perhaps reference other local schools that allow girls to wear trousers to show it is a no brainer.
I would not go too strong on the gender discrimination line, because some bright spark will no doubt say 'but then isn't it gender discrimination to say boys can't wear skirts?' (to which the logical answer is yes, but the practical answer is that the chance of one of them wanting to if no one mentions it is vanishingly small).
The governors will want to avoid making a decision that puts them at risk of making a load of other parents angry (e.g. deciding that to avoid gender discrimination everyone has to wear trousers), or ending up in the local paper as the school that allows boys to wear dresses. If you can present it as the option that puts them in no-risk of either of these, they should (if reasonable) go for it.
If they do not respond to this approach, then go for stinkiness, and photos in the local paper of sad girls with freezing knees etc...
