I've just contacted the UKBA and they said that you can continue to work under the conditions of the visa you have while your new visa is being processed. The information related to this can be found at the bottom of this page: http://www.ukba.homeoffice.gov.uk/visas-immigration/while-in-uk ...

I am currently employed under a Tier 5 visa and have applied for the FLR (M) extension. If my FLR (M) doesn't get processed before my Tier 5 visa expires, am I allowed to keep working?