How do I get my old toilet to work again?

My toilet wasnt flushing properly as it needed to be flushed 2/3 times for it to empty the cistern. I got a plumber out to fix it, and he complained it was an old cistern, but replaced all the internals with a new push button system.

The toilet then started to have a different problem. The cistern emptied, but the bowl now fills to the top, before suddenly emptying, but doesnt remove waste properly. The symptoms are like a blockage, but it seems fine as I have lifted the manhole and the water flows ok

Does anyone now what has happened and why my bowl fills to the top before it empties?

I'd like to keep my old toilet as it looks better with the rest of the old suite, and it is good quality