Immersion at St Helen's Spring (Sacred Spring in England)

I have been planning to take a group of visiting in-laws to various healing springs in South East England (related question here), and St Helen's Spring in Hastings seems like a great venue.

I have managed to acquire a great map to the spring as it's hard to find...

The 'x' on the map marks the location of a stone-built pool (presumably from the Victorian age) that captures and collects the water. The Trip Advisor site offers a photo of the pool, but gives scant information about it. The main Trip Advisor page for the spring gives an alluring description, but again nothing specific.

The Wikipedia suggests that the stone-build pool may have been used in the late Victorian age as a baptismal pool. And one source dates the construction of the pool to the 8th century, if not the Sub-Roman era.

Question: can tourists (or even local visitors) immerse themselves here without fear of violating a rule laid down by the Trust? Or even a public law? Is it ok to 'take a dip' there?

Note: I know (from the Trip Advisor link above) that the water is a constant 4 degrees year-round and taking a dip might be awfully cold, but surely if people were getting baptised there then it must be bearable.