State Pension from Switzerland and the UK, can you claim a state pension from both?

I have British and Swiss Nationalities. I have been living in Switzerland for approximately 30 years and during that time have made payments to their state pension system. In the UK I had already worked and had 6 years of full NIC payments. Recently I qualified for class 2 NICs payments and paid for 16 years backdated. I was at that time told by the HMRC advisor that I could claim a state pension in the UK and in Switzerland. I am continuing to pay my state pension contributions in Switzerland where I am employed, and also my voluntary NIC in the UK. When I retire in 8 years time I will be 2 years short of a full Swiss pension (which requires 40 years), and 2 years short of a full UK state pension. I pay tax in Switzerland on my income and global wealth, and also pay income tax in the UK from rental properties. In Switzerland the retirement age is 65 and in the UK it is 67. So my question is, in 8 years time when I retire, do I claim my pension from Switzerland at 65, and then make a separate claim my UK pension separately from the UK at 67? I am asking since the documentation is very complex and difficult to interpret: Convention on Social Security Coordination between the United Kingdom of Great Britain and Northern Ireland and the Swiss Confederation.

Hi Robert Taylor,
You will need to contact the Department for Work and Pensions, who will be able to answer the query that you have. 
HMRC has no say in when and how you can make a claim the UK state pension.
Please find the contact details for the International Pension Centre (DWP) below:
Number  +44 (0) 191 218 7777
Fax  +44 191 218 7021
Address
International Pension Centre
The Pension Service 11
Mail Handling Site A
Wolverhampton
WV98 1LW
United Kingdom
Open
8.00am to 6.00pm Monday to Friday, closed bank holidays and weekends
Thank you
 

Thank you. I will contact them as suggested.

Hi Robert - may I just ask what the response was? My sister is in a similar position!

Hi Robert, I'm also curious to know how you got on.