It might help, but there have been some massive petitions which the gov simply ignores if it suits them. Every option has to be worth a try. Raising it with your local MP might trickle through but it's a very diluted way to make a point and easily lost.
Any petition, or action, would need to include the dumping of waste in the countryside. That seems to have become a monster issue since commercial waste producers had to pay to get rid of their rubbish - it's so much easier to just dump it on someone's land, or on some country lane. It seems to be a feature of human nature to dump rubbish and forget about it - there's quite a lot dumped on the moon - bags of urine, faeces and vomit for example, uneaten sandwiches and bits of equipment not needed on the return journey - sounds like it was a great picnic!
I think expose programmes headed with the usual well-kent faces play a huge part, but then it's how to keep the impetus going once our indignation is fired.
The development of new technologies to allow plastic to be burned to produce power, whilst trapping the toxins and noxious gases given off, should go a long way towards solving our rubbish problems but of course they take time to set in motion.
I had thought that the rubbish sent overseas was going to proper, dedicated recycling facilities, and was a way for the accepting countries to earn a bit of cash - how wrong I was
They still haven't sorted out how to deal with the vast backlog of medical waste in Scotland which has been lying for months and getting bigger every day.