Welcome EllasFella - can't help but noticing that you live in Peterborough, which is flat. As such, after a few weeks you should have no problems getting about!
A good run is from Peterborough, using the cycle hub trails to go to Whittlesly and back - do that a couple of times a week and you should, after 3 weeks be able to do the whole circular hub in an afternoon.
As we are in winter and I appreciate you may not like cycling at night, you could both try swimming once or twice a week or going for a walk once or twice a week at a fastish pace (to get ever so slightly out of breath) then cycle at the weekends. Once the lighter evenings come then you can cycle more.
Don't worry about spending money yet on new bikes - the risk being that you may both get fed up quickly because of weather and a seemingly lack of progress that your new steeds will just end up unused like your last pair. As above, fit less aggressive tyres, put the saddle to the right height and your bikes will be less clunky. Once you are sure that you both like to cycle, then get a new bike. Just please stay out of Hafrauds!
You can get a 'single speed' style bike, but with gears - a bike equipped with a Roloff hub, Nexus Hub or Sturmy Archer hub will be absolutly fine. Racing bikes are light and fast, but also can be uncomfortable if you are not used to them. A flat bar, 700cc wheel size touring bike fitted with slick tyres would suit you perfectly. Bit like these two really!
Revolution Pathfinder Nexus '08 (Only available from the Edinborough bike co -op)
http://www.edinburghbicycle.com/ebw...QRY=C105&f_SortOrderID=1&f_bct=c003155c002910
or this one - Specialized Globe Elite '08 (available at any specialized dealer)
http://www.edinburghbicycle.com/ebw...QRY=C105&f_SortOrderID=1&f_bct=c003155c002910
They do 'lady' versions too