When I came to sell a piece of my garden to a neighbour a couple of years ago, I faced exactly the same problem. Our (joint) solicitor discovered a charge registered against my property, despite me having paid of the mortgage in 1995.
I had to do a lot of hassling (particularly as the Woolwich Building Society, to whom the charge was registered, didn't even exist any more!) but I eventually got Barclays (who had taken over the Woolwich) to confirm to the Land Registry that the charge should have been lifted.
In your case the solicitors are obliged to go by the Land Registry records, so you need to get the Halifax to formally remove the charges (rather than simply state that they shouldn't exist). So you need to keep hassling the Halifax. (Remember to make it clear that you require them to complete the relevant paperwork for the Land Registry and NOT to just send a letter, to you or to anyone else, simply stating that they don't recognise the charges).
If you still experience problems, threaten to involve the press. It's amazing how often that speeds things up!
Chris
PS: It could be worse. Several months after I'd paid the mortgage off the Woolwich tried to repossess my house because I'd not been making the monthly payments!!!