So how much is this all costing the British taxpayer? I understand and I'm full on board with collective defence through NATO, but this does cost a great deal of money. Is Estonia going to be contributing more?
The modern Estonian Air Force has been rebuilding the destroyed military infrastructure since 1994 when the last Russian Army units left Estonia. Most of the funds were directed to the Ämari military airfield which was completed in 2011. Due to the lack of modern and developed military aviation infrastructure the Estonian Air Force development has been very slow. All aircraft are unarmed.
https://en.wikipedia.org/wiki/Estonian_Air_Force#Current_inventory
The task of Air Policing is one of the main peace-time/non-wartime activities of today's Air Forces. Mostly jet fighters are used due to their large range of services at all altitudes and speeds, its comprehensive sensors (radar, IR, Data Link) and versatile armament. For slow and low-flying aircraft (gliders, balloons, helicopters) normally turboprop aircraft and helicopters are used.
Contrary to popular perception, air policing is one of the most complex and challenging tasks of the Air Force. Unknown aircraft must be identified within a short time and in all weather conditions with no margin of error and intercepted if necessary. Air policing is performed daily and is always a real commitment and not sidelined to things happening in parallel (such as air combat exercises). Air policing ensures the control and sovereignty of the national airspace and security in air transport. Thus, the Air Force not only carries out the tasks of an independent state but also acts for the benefit of civil aviation.
Some nations are too small to carry out this task in their airspace. For instance, Liechtenstein's air policing is undertaken by the Swiss Air Force. Other nations have not the equipment and/or the money for this task. These often have an agreement with another nation or belong to an organization such as NATO) or are in Baltic Air Policing or Icelandic Air Policing.
https://en.wikipedia.org/wiki/Air_Policing
The Baltic air-policing mission is a NATO air defence Quick Reaction Alert (QRA) in order to guard the airspace over the three Baltic states of Estonia, Latvia and Lithuania.
Within the Alliance, preserving airspace integrity is conducted as a collective task jointly and collectively using fighter aircraft for Air Policing. Air policing is a purely defensive mission. Since the 1970s, NATO has established a comprehensive system of air surveillance and airspace management means, as well as Quick Reaction Alert (QRA) assets for intercepts (QRA(I)) provided by its member nations.
This structure of weapon systems, control centres and procedures is referred to as the NATO Integrated Air Defence System (NATINADS).
NATO members without their own Air Policing assets are assisted by other NATO members. Luxembourg is covered by interceptors from Belgium, while Slovenia and Albania are covered by Italian and Greek aircraft.
Since March 2004, when the Baltic States joined NATO, the 24/7 task of policing the airspace of the Baltic States was conducted on a three-month rotation from Lithuania's First Air Force Base in Zokniai/Šiauliai International Airport, near the northern city of Šiauliai, and starting 2014 at the Ämari Air Base in Harju County, Estonia. Starting with the Turkish deployment, rotations changed to a four-month basis. Usual deployments consist of four fighter aircraft with between 50 and 100 support personnel.
The three host nations contributed €2.2 million in 2011 to cover the deployment expenses and are supposed to contribute €3.5 million yearly by 2015. In 2012, the Alliance allocated €7 million for Šiauliai airfield modernisation from the Security Investment Programme.
https://en.wikipedia.org/wiki/Baltic_Air_Policing
Then why do they fly near the Russian borders?
Because 93% of Baltic coastline is non-Russian. And because most international air routes run there. Define 'near'
http://schiw.sf.hs-wismar.de/siw/paper/heft6/mueller1
Intercepts happen all the time, on both sides. That is never been the issue.
The issues are a) what prompts the need for an intercept and b) how is the intercept conducted.
Starting with b), you'ld like it to be conducted in a safe and professional manner, than minimizes risk to any of the involved. As for a) if you fly without having provided a flight plan, if you suddenly deviate from a filed flight plan, or fly without active transponder, and/or don't respond to e.g. radio calls, any plane is a potential threat that needs to be investigated (keeping 9/11 in mind).