I hope I can help.
Are there any rights reserved on the register of title for the benefit of your property over the unregistered mews?
Have you done a land registry search to determine if the mews is actually unregistered?
Even if it is unregistered any easement should have been registered as a land charge against the unregistered land. It is possible to do a land charges search to establish this.
If no formal rights exist then you will have to establish a prescriptive right. This means 20 years uninterrupted use. Clearly you cannot do this as you have just bought the place. You would need to contact the seller to see if he/she would provide a statutory declaration confirming the rear access via the mews for a 20 year period.
if you can establish a right of access, either formally or informally via a prescriptive right then this cannot be blocked.
If you have any further details on the deeds to your property or the unregistered neighbouring property then I can assist further.
I hope this helps. Please do not hesitate to come back to me if you have any further questions or queries.
Have you enquired with the Highways department of the local authority, they can give you the status of the mews. Regardless of the status of the road you need to establish that you can currently access the property off the mews and that this has been done for some time. It sounds as if the rear of the property is currently fenced with no direct access on to the mews and that your intention is to install a gate in order to access the mews from the rear.
I cannot see how the developer can relocate the parking to the other side of the mews without permission. Do you know if this has been applied for?
You could apply for planning permission to install a drop curb - I am unable to comment as to the chances of success in obtaining this on the facts to hand. An application would take up 8 weeks.