It starts to get a bit complicated.
The first paragraph in LTN 1/20 about allocation of highway (the highway includes the pavements and verges) space specifically says it shouldn't come from pedestrian space, but main carriageway space, where possible. So the principle is there from the outset.
But some carriageways may be narrow already. The guidance does point out that while urban carriageways do
tend to meet a minimum of X metres wide (I can't remember the exact number), they needn't be, especially in e.g. residential areas where it may simply be accepted that low-volumes of large vehicles need to wait for a gap, that sort of thing.
For pedestrians the greater concern is often for wheelchair and mobility scooter users. Not just the pavement being wide enough for them to travel in a straight line, but having the width to account for a chair's turning radius, and also for two wheelchair users to pass each other. Ultimately, the DfT guidance says they should be at least 2 metres wide.
Of course, what we're often doing here is retrofitting cycling infrastructure onto roads which were never built for cars but unless you have a very strong anti-car will now need to accommodate cars and usually at least one row of parking. So highways authorities (local councils usually) make compromises and they say well this is outside a primary school so we should leave lots of room for pedestrians as there'll be a hundred families here at 3pm, but this road over here is on the border of a residential grid and actually very few people walk it so maybe we take 75% of the space for this new cycleway from the main carriageway, and 25% of the space from the pavement, and in the unlikely event two wheelchair users need to pass they can work it out. That
sort of thing anyway.
I've spot checked a couple of those and, imprecisely using the 'measure distance' feature on Google Maps, found they're often around 1.3m for pedestrians - sometimes a little more, often a bit less. Under the Disability Discrimination Act (before it was replaced with the Equality Act 2010), the recommended minimum was technically set at 1.2m.
To complicate things slightly further, public rights of way footpaths, bridleways, and byways are also highways, and covered by the Highways Act. The minimum width of a footpath in the act is set at 1.0m, unless it is a field-edge footpath, in which case it is 1.5m, and for a bridleway (can be used by pedestrians, cyclists, and horseriders), it is 2.0m or 3.0m respectively.
But.. all of this technicality aside, I would just look at the setup.
This is a screengrab from from the first Google Maps link, turned 180 degrees:
View attachment 184464
On the left, that is a bi-directional cycle lane. I'm not convinced I'd like to pass too many cyclists coming the opposite direction that space, especially stopping for every T-junction.
On the right is the pedestrian area. Apart from some people being too wide to fit through the gap between the sign poles, particularly some wheelchair or mobility scooter users, you also have the superstitious pedestrians who don't walk under signs. In any case, I am betting the majority of pedestrians would walk in the cycle lane side of this space.
If I were a confident cyclist (which I happen to be), I'm going to stick to the road, which is a 24hr bus/pedal cycle/motorcycle/taxi lane. If I were a not-so-confident cyclist, I might not bother cycling at all because neither options feel great or safe. I'd go as far as saying that a lot (maybe not a majority) of people who would use it are people who would cycle on the pavement anyway.