I am by no means an expert but I found the below on gov.uk. Welded shut to me would appear to be illegal as could fall under a permanent fence or a padlocked gate.
Keep public rights of way clear of obstructions
As the owner or occupier of land with a public right of way across it, you must:
avoid putting obstructions on or across the route, such as permanent or temporary fences, walls, hedgerows, padlocked gates or barbed wire
make sure vegetation does not encroach onto the route from the sides or above, bearing in mind the different clearances needed for users of different types of route, for example by horse riders
Obstructing a public right of way is a criminal offence. The highway authority has the right to demand you remove any obstruction you cause. If you don’t, the highway authority can remove the obstruction and recover the cost from you.
https://www.gov.uk/guidance/public-righ ... sibilities