I can't think of many disadvantages. I've read some things about increased fire risk, sound proofing, condensation between the layers and risk of the wood rotting but I think these have been cancelled out by the quality of the materials used and how much the industry has developed, e.g. breathable membranes as standard for condensation. If you have a Google for disadvantages then take note of the date of articles (e.g. something from 2008 is likely to be out of date). Most of the companies I've looked at have detailed information on their products and can provide strong reassurances of the quality of the product. Timber frames are used as standard in places like Scandinavia which encourages me. One thing to note is to check with the council's planning department for their general thoughts on timber frame and render as a method of construction (and maybe have a Google about banks lending for mortgages). I doubt it'll be a problem though.
We're going to use timber frame and I'm just about to get quotes from companies. We're doing a brick exterior and I'm guessing that the price will be less than brick/block given London trade prices.
Even if costs were the same or higher I'd definitely​ go with timber frame given the speed of construction, less reliance on the trade and the fact that we're project managing ourselves and need more guidance. I've been waiting for the extension for 2.5 years and counting (we live in a wreck) and the day the panel go up will probably be one of the happiest of my life.