Growing veggies indoors in winter - grow lights?

Supercell

I've tried to grow veggies in winter in the greenhouse last winter but while they did sprout they quickly died back, its just too cold outside.
The back of my kitchen faces southwest with big windows so I got one of those plastic greenhouses beside the full length window and thought that would be just the job. Pak Choi was my weapon of choice as it did best in the greenhouse trials last winter but they are just growing tall and spindly and reaching towards the light.
So my conclusion is either I heat the greenhouse or provide better lighting indoors where it's much warmer.
I think the betting lighting is the way to go so was wondering if anyone has some suggestions as to something cheap and cheerful that might do?

The Garden Shop

Hello Super cell

I can't advise on the lighting systems
But you shouldn't rule out the greenhouse heaters
You could use a paraffin based heater - cheap to run

They are a great way to get use from outdoor greenhouses in winter

You could grow:
Pak choi
Lettuce 'All Year Round'
Kale 'Darkibor'
Broad bean 'Aquadulce'
Carrot 'Early Nantes'
And Spinach

These are all hardy enough for winter sowing, but as you say yourself - they will need good light levels.