Well-eaten root vegetables

I have tried to grow turnips, carrots, radishes and mooli for the last three years, but I don't think that I am going to try again. They are all riddled with grubs and I can't get anything to eradicate them.
I even bought Resistafly carrot seeds and sowed young onions between the rows, but it didn't do any good.
I know the weather has been atrocious this year, even my aubergines have damped off in the greenhouse.
I don't have much growing room, so I will only grow things that I am sure of succeeding with, ie. peas, beans and courgettes, and tomatoes, cucumbers, chillis and peppers in the greenhouse.
I have been gardening for 50 years and never had so many problems.
Have other people had these problems?

 

lost the entire crop of leeks, some leafmining thinger got to them, then they turned to slime.

 

Saw a program on the telly where a guy who is famous for his allotment in Yorkshire, only grows carrots in tubs off the ground to avoid carrot fly, he pulled some huge carrots out to show and has won many prizes.