First of all, international medical graduates becoming a surgeon in the UK is not very common, as the surgical specialties are very competitive. But nothing is impossible if you are sport for it. Here are the competition ratios in 2021:
Cardiothoracic Surgery ST1
Applications submitted: :113
Available Posts:6
Competition Ratio:18.83
Cardiothoracic Surgery ST3
Applications submitted: :47
Available Posts:2
Competition Ratio:23.50
Ref: https://specialtytraining.hee.nhs.uk/Competition-Ratios
Now if you decide to be a Cardiothoracic Surgeon in the UK after finishing your MBBS and Internship. First goal is to always get GMC registration with a permit for practicing. Once you have obtained GMC registration first strategy should be to familiarize yourself to the NHS by performing jobs that are not training jobs. 
For GMC registration, please take this questionnaire on the GMC website: https://www.gmc-uk.org/registration-and-licensing/join-the-register/registration-applications/application-registration
There are currently two entry points into cardiothoracic surgery in the UK: ST1 and ST3
Here are the options you have:
Option 1) Clear both parts of PLAB and OET (Full form of OET- Occupational English Test), and then apply for GMC registration. After GMC registration apply for Cardiothoracic Surgery ST1
Option 2) Join MS or DNB General Surgery in India or Join as a JR in surgery department to gain some work experience of day-to-day nuances of General surgery. During this period, Clear both parts of MRCS and OET (Full form of OET- Occupational English Test), and then apply for GMC registration. After GMC registration apply for Cardiothoracic Surgery ST3.
Go through these links for further information
–https://roadtouk.com/training-in-uk/training-in-surgical-specialties/specialty-training-in-surgical-specialties/
–https://www.bmj.com/content/349/bmj.g5987
–https://wessex.hee.nhs.uk/medical-dental-training-recruitment/core-and-specialty/cardiothoracic-surgery-st1-st3-national-recruitment/
–http://ja297.user.srcf.net/useful-careers-resources/cardiothoracic-surgery-training/