I am employed by a US company but live and work in the UK. I also get paid into a UK bank account. Can I travel to the US with an ESTA and remain under the VWP for business meetings or short term work in the U?
The answer would appear to be no.
The US State department offers this flier on business travel to the US suitable for the B-1 Visa (and by extension the VWP) on their website about the VWP. While some of the activities you describe (meetings etc) would fall under the B-1, there is always the note of "no income from a US-based company", which you will be receiving.
Looking at the list of work visas to the US, I think the L-visa would be suitable, however it seems more foucssed on those who will remain in the US longer term, not just making short visits.
You should get your employer to contact an immigration specialist/lawyer and determine what you should be doing (and if a professional's advice contradicts mine, beleive the professional). Do not be easily dismissed by your employer to "oh, just come here anyway". If you are judged as breaking the rules, it is you who will face consequences (never being able to enter the USA without a visa again, treated with more suspicion by immigration authorities of countries that the US shares information with), while your employer is unlikley to face any consequences.