What line of work are you in? That's the main issue as to whether £19,000 is a reasonable salary. My advice is that if you don't ask, you don't get - so go back and ask for more. You'll need evidence of comparable salaries and present in a very positive way.
I think the average wage across the country is £23,000 pa, generally higher in London and the South East, and of course with huge variations across different jobs.
As to whether you could live with 3 kids and a husband on £19,000 pa in Lancaster - I'm sure you'd be OK, but you may want to check out the cost of housing first, which can be very expensive ... would you be eligible for University housing or would your employers give you any kind of relocation expenses??? The company car is a good deal - running a car in the UK is very expensive.
By the way, Lancaster would be a great place to live, especially if you like the countryside - this may outweigh any tightening of belts that you may need to do!!!