I think in all honesty, if you can find a public sector job and stick to it for the next 20 years, this is probably your best chance of having a reasonable retirement. There are a number of part-time options in the public sector. In addition, you'll probably need to contribute to your private pension also.
If there's any way you can up your contributions to £100 per month, that'll help. Also you should consider changing from the default fund to something a little more adventurous that is likely to grow faster. After all, with a 20-odd year horizon, you have time to ride out any drops in the market (which are typically only a couple of years long).
A quick run through a compound interest calculator (£5000 starting pot, £100 per month contributions, over 22 years) comes back with a value of £140,032.95 assuming 10% growth per annum. Now, to get that kind of growth, you'll need to be in a higher risk fund. 10% is a high assumption too, but the fund I'm in has done around 26% in the last year alone, so maybe £140k isn't an impossible target.
Ideally, if you can reach a few hundred thousand at state pension age, then you're going to be fine. What's the situation with your partner's pension? can you both live off that?