Unfortunately, that's what happens in gardens, especially when they've just been planted. The new topsoil may have had weed seeds in it, and your garden soil will definitely have had weed seeds in, so after planting, regular use of the hoe or border fork to dig them out is required to keep the weeds down, preferably not leaving them on the soil, even if they've been uprooted. Over time, if you've had shrubs and perennials put in, they should grow larger and there'll be less opportunity for weeds to grow, but they will still grow, or try to. I'm afraid a garden requires regular maintenance, even low maintenance style planting.

Well you know the difference between clover and cress, so that's a good start! Now is your opportunity to stop being hopeless - there's all the help and advice you could want on this site (except getting somebody to do it for you!)
Keeping a garden neat is a long succession of pulling up little weeds before they turn into big ones but the rewards are tremendous!

I would suggest that you get weed preventer and sprinkle it on top of the soil (read the instructions). This prevents any still unsprouted weed seeds from germinating. It can do nothing to stop any weeds you see but it will stop the second wave from coming up. Apply every three months and you should get good results. I'm from the USA, so I do hope that this is available to you in the UK.

Well not heard of it Loosestrife, maybe others have. ....

I never used any of that stuff (herbicides, weed preventer) but I'm in my mid 80's and I can't wield my garden broadsword anymore.

Not available in the EU or the UK, Loosestrife. I have to say I am aware that, in the States, there is a great deal more use of herbicides and pesticides, with a wide availability of products we've never had here, and likely (and hopefully) will never have. Luckily, generally speaking, gardens here are much, much smaller than many 'yards' in America, making physical weed management easier.

Kaztastic - I've had a lot of maintenance work over the years from gardens I've planted - I never really liked maintenance work unless it was a garden I'd planted myself with low maintenance stuff, but in the first two to three years, regular maintenance is necessary, and clients always want that service, in the main. Sounds like you might be one of them, so you might want to consider finding a gardener locally who'll come in to keep it under control till it all grows on and the maintenance becomes less if you don't want to do it yourself.

I seem to remember that there used t be a pre-emergent weedkiller in the UK - possible on the banned list now.

Years ago, there was a product you could put on lawns to kill earthworms so your perfect lawn was not disfigured by worm casts in autumn and spring, for heaven's sake... I never used it, and it disappeared a long time ago. I've never seen a pre emergent nor a weed preventer available in this country, so it must have been a long time ago Steragram!

Well yes, I guess it was...heard about it on a radio gardening programme...