I wouldn't count things like saving for annual bills, car ins, car maintenance, house ins, Christmas, birthdays etc as savings. That's just budgeting really. We worked out roughly how much each of these type things cost and added 5% to be safe, have a separate pot for each that gets paid into monthly. The money is there when needed. It did take a bit of time to get to the point that I could do all annual expenses like this.
As for savings we are lucky to be able to put away approx £1400 a month for medium to long term savings. Medium is larger house projects such as new bathroom, windows, carpets, garden etc. Long term is for additional money in retirement. I want to be able to get someone in to do the garden, paint the house go away for a long weekend at the drop of a hat without worrying about where the money is coming from.
We also save into regular savers each month and at the end of the term transfer to an ISA. The money in these is for car purchase in the shorter term and for the other longer term to help with health costs in later years. I would like to have the option of better than NHS for things like hearing aids if needed, private physio or a cataract op etc. Could never afford full private health care so this hopefully would make a difference to some aspects.
We both have full state pension when due and also have okay works / private pensions. The longer term savings mentioned above are just to give that bit extra comfort.
It has taken a long time to get to where we are. 13 years ago we had £15000 of credit card debt. We were only just scraping by and lived hand to mouth most months. Now our mortgage is paid off, partly because we chose to stay in a house that many on here would deem small, one bathroom, one living room, no separate dining room etc. We could have moved and had a house twice the size but we decide to prioritise financial security instead.
The best thing I ever did was go onto the money saving expert forums. People on there give great advice on debt, savings, pensions all without the mumsnet 'is this a stealth boast' crap. There's none of the immature jealousy on the money section that you get here. If any do pop up they are generally politely told to stop.
I read the advice on how to save, how to pay down debt effectively and how to budget and I put it into practice.
Sorry it is so long. I just wanted to show that it is possible to get from having not a penny in savings to being in a okay position.