In situations like this, my advice is always to consider things from the company/HR point of view!
In almost all cases, the biggest cost for a company is the staff! So from an HR point of view, if you can get people to do more for less money, then you are doing your job well. Even if ultimately they have to back-pay you, a few months not paying you at the new rate, is a few more months with the money in the company account which pays interest and they have ultimately saved money, so they will always delay as long as possible and pay you as little as possible and so they should - its their job!
Its up to you to do something about it, because if they are doing their job well, they should be screwing you as much as possible for as long as possible! The longer you take it, the better they are doing their job []
My advice is always to be upfront with them! Sort it now or I don't do it! Don't take any sh1t, contracts can be drawn up in a few hours if needed, make sure they back-pay you to when you started the new role and if necessary leave - there's plenty of other jobs around if you've got the confidence to get off your ar$e!
Just think what excuses you would come up with if you didn't want to pay someone more money and you can be sure their excuses are better! Don't believe any of it and make it clear you know what their game is! In the end you'll find it benefits your career as they realise they can't take the p1ss!
As for unions, stick well clear! Unions are only interested in increasing their own power and feeble attempts at making life better for the masses, including the lazy gits that don't deserve it. Given the choice, they will quite happily sh1t on an individual (you) for the percieved benefit to the union or the masses!
Just my 2p, but I think I've done alright since turning by back on the corporate masses and forging my own way in life! []