We have just gone through this process twice, once for me last year and for the rest of the family this year. I did my application through the (now cancelled) HSMP, and the biggest problem was getting the visa approval. One day I may tell that whole story but I am sure nobody wants to hear it now. In any case, once the visa application was approved I applied for entry clearance to the nearest consulate via express mail. This whole process took less than five days. Most applications can be done online:
http://www.ukvisas.gov.uk/en/This year the rules had changed, and the process was easier. We made the online applications, then there is an appointment to take what they call "biometric data" (doesnt that sound impressive? it's a photo and fingerprints. doesnt eliminte the need to send them a photo for some reason.). Then off went the applications, and once again everything was approve and returned within five days. These were for dependent visas, not for the permit itself.
So I would say that unless you think there is a chance that your work permit will not be approved, it should be fine to go ahead and make travel plans. The Home Office does give stats on how long an application generally takes. I am too lazy to look them up now, but seem to recall that once the application is received they generally do not take more than two weeks or so.