We have a Witter ZX88 which costs about £100 which I have used on my car but don't have a tow bar on the MH. You need to have a way of locking the bikes and holding them down onto the tow bar bracket as the vertical pole can be lifted off otherwise and the bikes nicked if you leave enough vertical slack. Chain or cable locking the bikes to the tow bar would be best if possible. You would probably need a lighting board and extra number plate as the MH number plate would be obscured but presumably you have towing electrics so can achieve this.
We have Thule 2 electric bike model that works fine. It's a bit deeper to allow for electric bikes. It's very substantial and weighs about 20kg so a bit of a lump to move around. There is a very good locking arrangement on it.