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If you’ll forgive one supermarket recommendation, the 2015 Graham LBV is excellent and much better than previous years. It is sometimes on offer and so really cheap. I’d highly recommend stocking up on it if you can find it.
In terms of interesting and affordable Ports which aren’t available from supermarkets, I should start with a significant disclaimer: Port is often sold for a ridiculously low cost by British supermarkets (sometimes even as a loss-leader) so if you start looking for wines that are more unusual, you will struggle to find ones which represent quite as good value.
Some suggestions:
2014 Tanner’s LBV made by Churchill’s which is
£17.20 a bottle. I might also be tempted by their 2006 Crusted, also by Churchill, which is £23.50.
One of the Niepoort LBVs.
Uncorked has the 2014 at £21.50, although if choosing blind, I’d go for a 2015 if I could find one. They also have the Niepoort Crusteds, although those aren’t particularly cheap and the Martinez 1985 VP which I haven’t tried in the last decade but which will give you an impression of a fully-matured VP at only £30ish.
The Quinta do Infantado 2015 LBV which
Nickolls and Perks has for £21.60. This is a traditional Portuguese LBV: it’s essentially a Vintage Port that has been bottled late. The Infantado Ports are also interesting since they try to use as little spirit as they possibly can.
Majestic usually stocks the Taylor’s SQVPs. The Quinta de Vargellas is the most famous from the main property in the Douro Superior but you can also find the Quinta de Terra Feita which is a bit cheaper, rarer and often excellent. They also sometimes stock some of the other Taylor Fladgate Partnership SQVPs like the Croft Quinta da Roêda which is excellent value, although I think you sometimes see that in supermarkets too.
I’d also suggest trying the Quinta de la Rosa and Quinta do Noval LBVs and the QdlR VP if you see them, despite them being supermarket Ports, too. The Warre unfiltered LBV—again another supermarket Port—has consistently good reviews although I’d only buy it when it is significantly discounted.