What are the best states to retire in which Social Security is not taxed, income from pension is not taxed?

It is rare to find a perfect place. Florida, Nevada, Tennessee, Texas, Washington state are potential states. Florida often has humid summers but people flock from New Jersey to areas in Florida such as Orlando, Boynton Beach, and the space coast area. Texas cities have some potential where Austin, Dallas-Ft Worth and San Antonio are possible choices. Reno in Northern Nevada fits some of your criteria well. Nashville and Memphis in Tennessee. I chose Las Vegas and there are many retirees here in the valley.

Details follow:

Alaska, Florida, Nevada, New Hampshire, South Dakota, Tennessee, Texas, Washington and Wyoming have no state income tax. Illinois, Mississippi, Pennsylvania supposedly exempt pensions, but I did not look up details of which pensions are exempt.(only 13 states impose tax on Social Security income: Colorado, Connecticut, Kansas, Minnesota, Missouri, Montana, Nebraska, New Mexico, North Dakota, Rhode Island, Utah, Vermont and West Virginia)

Activity is city and region rather than US State. Many states have large unpopulated areas. Employment and even weather get down to specifics.

I live in Las Vegas. I bought a 940 sq ft condo for $100,000. No income tax. Property tax $46.24 per month, sales tax varying by item, Homeowners Assn fees $374/month. Electric averages about $70/month. Insurance about $100/mo home and car. About $590/mo plus phone, cable tv, internet are the base costs to live now so total typical under $700 baseline. All else is extra. Amenities and security-7 foot wall plus metal spikes around the large development with three gated entrances 24/7 manned and guest lists for entry plus roving security. Free community washers and dryers plus my own personal ones. 5 community pools (1 heated), hot tub, exercise equipment room, community gas grills, hot and cold water included, trash pickup included. excellent landscaping, centrally located near north Strip, I have no garage but large excess of private uncovered parking unassigned. Fresh fruit and vegetables from Mexico, California, and far-off places. Great restaurants in every price range including buffets from $8 to $50 per person. In my fridge is leftover New York style pizza comparable to the best in New York City ($19 17" 8 slice 3-meat). Discounted shows, community events, IMAX theaters, great shopping, over 300 sunny days a year (only about 5 inches of precipitation a year). Mild winters BUT baking hot long summers. August 2019 had a record 24 days at 105F or more with high to 112F. Using daytime high of 97F or higher as "summer" (This year June 4 through Sept 16), 105 days, Average high 102.72 and high temp never lower than 89. It is arid, like much of the desert southwest. People here are generally liberal Democrat, with a mix. Many Latinos.That stated as where I am, to show evaluation. Unemployment is relatively high and payscales low. Waiters and waitresses do OK here because no offset from minimum age and gratuities earn well.

It doesn't work like that.

States need money to operate.  If there are low income taxes, the money has to be made up somewhere or the service won't exist.  As a result, most places that have low/no income tax have high property taxes.

You might get both no taxes and low property tax in Nevada, but the costs are just added in elsewhere = they have excessively expensive utilities.

Or you can go to a place like Louisiana with low taxes and low property taxes, but have very poor schools and social services. 

There are no states in the United Kingdom.