You could have a 5 Tooth Bridge fitted to fill the three gaps you now have, but I would get a second opinion from another Dentist and get them to review an X-Ray. If your current Bridge did not hold you may have the same problem again if you were to have another Bridge. I would check the bone density and the strength of the two teeth that would be the new posts.
Alternatively you could have an Implant with a Bridge, having 5 individual Implants is not necessary, but one or two Implants would be more than enough support to hold a Bridge.
Our Implants are 945 GBP complete with Abutment and the permanent Crowns are either 225 GBP or 305 GBP depending on the Crown type you choose to have.
I wouldnt advise having a Denture, I would either replace the Bridge or have Dental Implants.
A five unit bridge is a very long span. If those supporting teeth follow what your others did, it would leave you with a real problem.
What your dentist is proposing is sort of "middle ground" between a partial denture, which can be incredibly natural looking and quite comfortable, and implants. If you haven't considered implants, I highly recommend them.
If the posts in the supporting teeth don't hold the new bridge, implants would be your only alternative to a partial denture and you would have already had the cost of the root canal, posts, and bridge.
The initial costs are a bit higher for implants than a bridge, but overall if you are a relatively young person it may be more cost affective.
Just a thought. I have four on the front top and love mine.
Good luck in whatever you decide and do let us know how you do.
Best to you,