The way to stop self seeding is by cutting all the dead flower heads off before they have a chance to produce seed pods, which b t w are poisonous, depending on the height of the tree, you may need a ladder, plus long handled loppers, just take off as many as you can, which will reduce the numbers, "no seeds, no weeds"

Rather a challenge with a 25 year old laburnum and does not answer the Q Derekm. Not sure what the solution is to only flowering every other year but pull up any seedlings as soon as you see them - this happens with most trees you just have to keep weeding them out.

As Mg says you just have to keep weeding them out. We have the same with ash, birch, holly, acer,cotoneaster etc, etc. All lovely trees but we cannot stop them seeding - just weed them out.

25 years is quite old for a laburnum, but there is still some life left. If you wanted to plant a new tree (not in the same location), which did not create a problem with the poison and seeding itself, then Laburnum × watereri 'Vossii', does give good flowers but very few seed are set.

I would be thinking of collecting a few seedlings and growing them on to replace this ageing Laburnum when the time comes.

The first part of the question is a statement that the tree only flowers biennially, the question was how to stop the seeds from germinating all around the tree, as laburnum only grow to between 10 and 20 feet high, depending on variety, I don,t think that what I suggested is much of a challenge, and answers the question as asked.
The biennial flowering is probably due to a deficiency of 1 or more nutrients, and requires a detailed soil analysis to find out which, but this question was not asked.

Laburnum alpinum ‘Pendulum’ only grows to about 2.5 metres others can grow to 7 or 8 metres. If you are agile I guess you could get up there to prune the flowers off.

Mg I did say as many as you can,!!!!

Indeed I had missed that... Actually a laburnum should be easier to deal with than an ash, beech or birch. What worries me more in Scotland is that SNH (At least I think it is SNH) has set up a rule that if you allow non-native species to escape from your garden you can be prosecuted. I understand the logic - think of giant hogweed and Japanese knotweed - but am not sure how to stop the birds eating the Sorbus cashmeriana, the Cotoneasters and all the other non natives in our garden and spreading the seed. Then there will be wind borne seed, I suspect SNH will have a hard time proving which garden something has come from!

Could biennial flowering in a normally annual situation, be something to do with water levels rising and dropping? Otherwise laburnums seem to be pretty happy in any soil conditions. As derekm says - every part of this plant is poisonous; though I add that the seeds are especially so. Take care of dogs in the garden that like to munch - not all dogs do, but some will pick up the smallest bit on the lawn just for a chew!!

Very hard indeed, I would have thought, lol

If they are determined, DNA is an option.............
I would have thought that the cost would be prohibitive though.

DNA? Well I guess they could but by the time they 'discover' the rogue the original garden plant might well
be long dead.

MG - nothing would surprise me any more!

I have a friend who works in the forensic industry in the DNA field. They have done just such work for a local authority, although I've yet to worm which one out of her (and I sadly never will........).