I understand why you think it should be "laid off", but I think the BBC version is fine. Why? Because the companies have not yet laid anyone off, so nothing has happened in the past. They cut salaries so that they didn't have to lay anyone off. If you add the word "more" (which would assume they *have* laid people off), you might see what I mean: "It showed that many UK companies, particularly smaller businesses, have cut wages rather than lay off more staff."

Excerpt: "It showed that many UK companies, particularly smaller businesses, have cut wages rather than lay off staff." The BBC is correct in their usage of "lay off" instead of "laid off" . You are correct in realizing that the verb "showed" is in the past tense. The rest of the sentence changes tense, because it is explaining what "it showed". (that many UK companies........... have cut wages rather than lay off staff.)

I'm no expert on grammar, but I think their sentence is fine. I understand your concern though because you want to see uniformity in the tense. "Have cut wages" your mind wants to see "laid off", both past. But in this construction, the sentence uses a past tense (don't know which one, as I say I'm no student of grammar) for "have done something" and uses something like a present perfect or present continuous, for "lay". But the reason they do it, is because one action has been committed, "the reduction of wages", and the latter part of the statement is detailing what was an alternative when they made their decision. "Will you cut wages or will you lay off staff?", "we decided to cut wages rather than lay off staff". "Laid" is only going to be used if you're telling people when you actually did it. "I laid off staff last year". Other than that every other time you'd use lay, "I need to lay off some staff", "when did you lay off your staff?". Sorry if this explanation isn't very clear.

@Pekka: The phrase "rather than" causes all kinds of problems. There is often no one "correct" answer. When you get time, do some research on the Web. It is quite possible that you may be correct in wanting to use "laid off." Some articles on this subject say that whenever possible, both verbs on each side of "rather than" should be PARALLEL. Here is an example from one grammar book: His father was disturbed to find that the boy HAD LIED rather than (HAD) told the truth. (Although you would not say the second "had," it is the reason for using the past participle "told.") Thus, MAYBE your sentence should read (as you said): Many business HAVE cut wages rather than (HAVE) laid off staff. (The "laid off" is not the past tense; it is the past participle.)

That's an interesting question and I am not sure if I have the defintive answer. The BBC version sounds better to me than yours, but I would not like to be categorical. For example we if just slightly change the sentence to: "It showed that many UK companies, particularly smaller businesses, have cut wages and not laid off staff." Pretty clearly in this case your version is correct and the use of "lay off" would be incorrect. So what's the answer? I don't know - just don't construct awkward sentences like the BBC!