The British native lime is Tilia cordata. The mainland European one is T. platyphyllos. They're obviously very close relatives because they hybridise, but the hybrid wouldn't naturally occur in Britain because the two trees wouldn't have been able to meet without man's intervention. It's mostly the hybrids that have been used for urban planting schemes.
There's a bit more about native trees - "Compared with other countries, Britain has relatively few native trees; between 30-40 (the exact number depends on how you define a 'tree' and 'species')" - and how they are managed on the FC/Westonbirt site http://www.forestry.gov.uk/forestry/infd-6zpgub including mention of a 2,000 year old T. cordata.
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