Mr Senington said his team had plenty of experience dealing with the seasonal spike.
"We have increased staff for a few weeks over the main period and we have increased our visits to top holiday spots."
The council has also provided 180-litre bins in popular areas for holidaymakers to put their rubbish in.
He said tourists were for the most part tidy and respectful of the environment.
"Most of the tourists we have do respond as well as we expect."
Mr Senington said the recycling centre was expected to remain busy until early February.
A waste reduction expert said councils were doing their best to reduce landfill waste.
Envision managing director Matthew Luxton said councils had a difficult role.
"Councils do the best with what they're given and councils have to deal with the packaging manufacturers create. That's a hard position to be in, especially for smaller councils, and I'm in full support of the councils."
He said people should always remember the "waste hierarchy" - reduce, re-use, recycle.
"Think: Do you really need to buy this item or not?"
People could also reduce waste by buying in bulk, which meant less packaging than individually bought items.
"Recycling should not be the first option for people, it should be the last resort after reducing and re-using," Mr Luxton said.