Harvesting seeds

We have been planting our cucumber seeds today and was wondering,if we saved the seeds from the cucumbers we grow this summer could we use them to sow next year?We do it with the runner beans and it works.
We also bought a tomatoe back from our greek holiday last year and saved the seeds,would they grow?
Just looking at saving money on seed buying 

I think we should all be saving more of our own seeds - they are getting so expensive to buy!
A bit of variation if they have cross pollinated is not a bad thing - we don't often want to harvest everything at once like the commercial growers most seeds are aimed at.

I have even gone astep further and allowed some things to self seed then moved the seedlings to where I wanted them. Worked really well with Rocket, Lambs lettuce and land Cress, haven't bought seed of these for 6 years!

Leeks you do like onions: let them stay in the ground overwinter and bolt in the spring.  Unless you're doing several types or there are ornamentals around, you should be safe from cross-pollination problems.

Sweetcorn will be a royal PITA: unless no-one is growing a different variety for half-a-mile around you can't guarantee true-breeding, and random crosses are very unpredictable.

Curcurbits, runner beans and peppers all need isolating, or you'll get some very odd hybrids (interspecies hybrids in the first case)!

Leeks you do like onions: let them stay in the ground overwinter and bolt in the spring.  Unless you're doing several types or there are ornamentals around, you should be safe from cross-pollination problems.

Sweetcorn will be a royal PITA: unless no-one is growing a different variety for half-a-mile around you can't guarantee true-breeding, and random crosses are very unpredictable.

Curcurbits, runner beans and peppers all need isolating, or you'll get some very odd hybrids (interspecies hybrids in the first case)!

You can save your own sweetcorn seed if it's not F1 hybrid (progeny can vary enormously)
but need a good season to get it to ripen and dry off

leeks are not difficult, they flower in the second year, I had some self seed ie seedlings sprang up around one which flowered the year before

TRY   IT OUT and report back??
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Oh this sounds good.

Well the leeks and sweetcorn are both from realseeds so any seed saving should be true to type.

So with the sweetcorn would I need to make a isolation cage like I do for peppers .

I was planning on growing 2 different types of leeks Bleu de Solaise and Jaune de Poitou  Yellow Leek so I'm assuming that will make things difficult.

Any advice would be very welcome