Thanks to the Met Office seamless integration of weather observations and forecasts can be made into your website. Via Datapoint just about all of the forecast information available on the Met Office website is available in XML or JSON format after signing up for an API key (registration is free).
After that it is simply a case of using your favourite scripting language to request the data and format it as you wish. I took the inspiration for this from Lorna Jane Mitchell’s blog and used PHP to include text-based forecasts into this site. Take a look at the weather page.