Parking dispute on Manor Terrace

We live on Park View LS25 7AX and we have a public road in front of our house and a public road to the back of our house (Manor Terrace LS25 7AU) and we use our back door as we cannot open the front due to a sofa in the way as it goes straight into our living room. We park our car on the public road at the back like we have done for 27 years of living there. Recently we have been having problems with 2 neighbours who live on Manor Terrace saying we should not park on their street as it is their access. We have tried to explain that it is our access as well as its access to our back door. One of the houses owns 3 cars, 2 work vans and a big campervan and they expect to park all of their vehicles on the public road (which takes up all the street) leaving us nowhere to park. The pictures is how they keep parking their campervan/vans and cars. The path is only a thin pathway so when my daughter visits with my grandchildren it is hard to get the pushchairs out of my garden, having to put the pushchair on the road to put my grandchildren in. Both neighbours think that we should be parking on the street at the front of our house and not the back. (There is no room at the front due to the amount of cars already parked there as they mostly use their front doors. As it is a public road at both sides am I right in thinking we can park at either side of our house and have as much right as our neighbours on Manor Terrace to park on the back street? When we can we park outside our own gate at the back which does not block anyone's driveway or cause any obstruction but our neighbour likes to park his 2/3 cars there so his cars are on his camera. When we cannot get parked outside our house we park in the next available space. We have today come out to a letter on our car telling us we should not be parking on "their" street and should be parking on our street round the front. Have they got the right to tell us where to park on a public road when we cause no obstructions to anyone else and can we park on the back of our house, have they got right to park a big campervan on the street which it wide enough to obstruct emergency services getting down the street or have the right to block our gate so we cannot get out with pushchairs? This is causing a lot of upset within our family and we just want clarification on the matter. Further pictures can be provided if needed.