You absolutely cannot just divert a public footpath because it suits you.
However, there is nothing to stop you creating a 'permissive path', being the path you would
like walkers to take, and offering it to them as an option with a friendly sign explaining what you have done and why. The majority will be happy to comply I'm sure, provided they don't feel that they are being bullied or that the official path is being obstructed or quietly eradicated.
There may well be a local Rights of Way group. Personally I would try to get them onside with the permissive alternative path approach. They will almost certainly work with you - after all, you are creating a new path and not attempting to remove an existing one
- and, being organised, they can ensure that the existing path is used sufficiently often to maintain the public right of way (but hopefully without unnecessary disruption to you when the land is waterlogged.)
If you do feel you have a case for a permanent diversion of the route you will need to follow a legal process. I remember a little about all this from when I was Secretary of the local Rights of Way group near Devizes. Most people chose the 'alternative permissive path' approach as it cost nothing and solved the majority of the problem, whereas the costs for an official permanent diversion began with a £1200 statutory application fee (in 2005), payable to the Council, which covered the costs of the publication of the proposal in the local papers, which was a legal requirement.
If your local RoW group and/or Ramblers or other walking organisation is/are a bit militant towards landowners, then of course they will regard any obstruction, whether physical or verbal, as a call to arms
. However there is nothing to take umbrage at in the creation of another, permissive alternative path, provided the original remains usable.
You may wish to take some advice on how to ensure that your alternative permissive path doesn't become a permanent public right of way
in addition to the existing one - I think it will be something along the lines of you close it for one day a year, but do check.