It would be a lot simpler if you used a Solicitor, as the following needs to happen-
A Land Registry Transfer document needs to be prepared and signed by both parties. Your ex wife's Solicitor would then agree to release the signed Transfer to you/your Solicitor on condition that you/your Solicitor hands over the £100,000.
Us Solicitors can rely on each other's Undertakings to deal with the above, but if you don't use a Solicitor, you may well have to send your ex wife's Solicitor the £100,000 before he then forwards the Transfer to you. Provided you get a letter from him, confirming that he will release the Transfer to you as soon as he receives your money, you will be fine.
The Transfer then needs to be registered at the Land Registry.
SO, unless you are familiar with Land Registry procedure and documents, you are best to ask a local Conveyancing Solicitor to do all the above for you. He is likely to charge approx. £350 plus VAT and there will also be a Land Registry fee to pay, based on the value of the property which is likely to be between £40-£90.
I hope this assists you and sets out the legal position.