Tree root killer

Use gazoil, but it is not ecological. The best will be to cover the remaining base trunks, this way, the trees will not find light to grow again. This process could take 18 month. I will suggest to put also Aguafuerte, an acid used in house cleaning. Then cover all the trunk basis.

The only sure way to kill the roots off is to grind them.

The roots ? How do you do ?

If it's possible, use a tractor, a chain, and extract the trunk and its roots. This is the real way to take off a tree. In many case, not enought place, and not a tractor in our tool set.

The simplest and probably cheapest method is to bang as many copper nails into the root stumps as possible. This will kill the roots but may take some time. On the plus side it’s very ecological and safe to the environment. 
(Banging multiple short lengths of copper pipe into each stump also works).

You can hire a grinder from The Hire Centre in Torrevieja, but sorry, don't know about Aspe.

Or copper sulphate..... 

Mix the copper sulphate with a decent neat weedkiller (glyphosate, round up, gallup etc) to a thick paste. Drill a few 12mm holes, 100mm deep. Fill the holes with the paste and cover. 

This stuff will work but will kill any nearby plants if you're not careful. Wear gloves and keep the mixture away from yourself, children and animals.

Problem, the copper sulfate is a venon for the soil, the copper, so it would be best the nails, put on the trunk and easy to take back. I never use both, copper sulfate or nail. Not only the copper is a pollution for the soil, but also damage the beneficial fungus of the soil.

Copper sulfate is used against fungus, and vignard and grappe essentially, for the leaves and branches.

I had some silver birches cut down but could not pull out the roots due to close proximity to the house. I drilled all visible roots and stumps and put diesel in some and neat Roundup in others both have worked equally well and I don't get suckers any more and some are rotting.

There is nothing else growing nearby so I'm not bothered if the soil gets spoilt.