Yes and no. We pay the equivalent of £500 a month but we have a really small flat, 55 square metres/600 square feet. (DS' bedroom is too small for a double bed, our kitchen is in the living room, no dining area, bathroom you could wee into the toilet from the shower while brushing your teeth looking in the mirror kind if size.) Looking at Rightmove you can find similar priced/sized properties for rent in Britain in cheaper areas, but not most areas. It's hard to compare because in Britain we don't classify rental houses/flats by square footage. I don't know how our town compares to other German towns. The going rate here is roughly €10 per square metre, so we are in fact overpaying (€700).
There is no council tax, which would be another £150 or so IIRC on a small property and some bills are often included in the rent - for example our water bill and gas central heating bill are included, but we pay our own electricity, internet, phone, etc. There is often a service charge for the building (extra to the rent, but not optional) which may include some utilities but usually just covers things like lighting and maintenance of communal hallways.
It costs a lot to move here. We are looking at about €4k next time we want to. This is because estate agents can charge a massive whack of commission, usually 3.5 months' rent. Then there is the security deposit and first month's rent in advance. And then Germans tend to take the concept of unfurnished flats to the extreme, so you have to buy a kitchen and light fittings, or sometimes you can buy them from the previous tenant. There are laws going through to limit the amount of commission it's possible to charge but very slowly. That said, renting is very secure and people often rent for much longer than they do in the UK.
Childcare seems cheaper but we don't use full time childcare. For Kindergarten, ages 3-6, 7.30am to 2pm we pay €97 (£69) a month. It's state subsidised. I don't know the costs for all day or for younger children. When he starts school this year we will pay €47 a month for school dinners and he will have care from 8am to 4pm. The school dinner is mandatory for the full day school. Some children attend 8-12 and go home for the day so have lunch there.
The Euro has dropped a LOT in the last year, so it might just be that until recently the difference wasn't that marked, but wages/cost of living haven't gone up as dramatically. £18k currently is about €25k. When we moved two years ago £18k was more like €21k. Depressing if we keep comparing, because DH has had several pay rises since we moved, but the rate compared to the pound has probably stayed about the same!