Hello Costa. I cannot give final advice on what you should do - that decision is up to you - but I can add some further ideas for for you to consider. Let me consider some points, one at a time.
Should your parents relocate?
You want your parents to move near you, but not actually live with you. I quite understand why you think that would be an attractive arrangement. Just one point of slight warning. Elderly people may sometimes be unsettled by moving into an unfamiliar area. However, if they are already familiar with the area where you live and are enthusiastic about the idea of moving there, there should not be a problem. I presume you cannot move to where they are because of your job.
What type of accommodation?
It sounds as though you favour the idea of a retirement home, and do not think they need a care home at present. You could also consider warden-monitored sheltered accommodation. A rented dwelling could be a stopgap solution to get them into your area quickly without waiting for their house to be sold, but other than that, it would not have any real advantage over an ordinary house. Round where I live, the rental for a small house would be around £800 per calendar month, possibly more depending on location. A care home could cost this much for a week. My own assessment of retirement homes is that they are very suitable accommodation but not particularly cheap. A two-bedroomed appartment would be roughly the same price as a three-bedroomed semi-detached house in the same area. There are charges on top of that; service and maintenance charges, and I expect ground rent because I imagine these properties are sold on a leasehold tenure.
Should you part-exchange?
There are expenses involved in selling a house - estate agent commission, legal fees, etc. If you part-exchange, these expenses are taken off your hands. Therefore you cannot expect to receive as much for the house as "expected market value". However this would get your parents moved into a retirement home quickly and with little hassle, and would avoid the expenses of stopgap renting. Another warning: selling a house at a distance is more difficult and has more pitfalls than selling locally. I once moved 300 miles to start a new job, but it took quite a while to sell my house. At that distance it was difficult to keep control over surveyors and builders doing remedial work, and some fittings were stolen, so I felt I lost out a little.
Summing up
Overall, therefore you need to balance the costs and benefits of one option against another. It may not be a bad idea to approach a retirement home organisation and get an idea of costs of accommodation and how much part exchange you could expect, but don't commit to anything until you have considered all options. The time is also ripe to start talking to a conveyancing solicitor, and discussing with them all these options and the legal position. If you have Power of Attorney, involve your parents as much as possible in all decisions. It is their house, after all.