Firstly there's the measure used: "Northern Europe". This usually means the geographical area that includes the Netherlands, Lithuania, Denmark, Sweden, Finland, Latvia, Britain, Estonia, Iceland, Norway and the Faroe Islands. The latter three countries are not in the EU and so are not measured by Eurostat, which makes it difficult to judge the veracity of the statement.
The above image takes northern Europe to mean France, Germany, Belgium, Holland, Luxembourg, Austria, Ireland, Sweden, Finland and Denmark as northern European countries and our "near neighbours". Looking at those countries, the statement is true. But those countries are not actually in northern Europe, nor are they typically used together as indicators. It also excludes other "near neighbours" such as Italy, Spain and Greece, all of which have regions that are poorer or just as poor as the UK according to the Eurostat data.
The poorest region of Britain, according to Eurostat, is west Wales, with a GDP per capita expressed in purchasing power standards (PPS) of 64 in 2011. Latvia, also in northern Europe, has a GDP of 60 (PPS) in 2011. Looking at France, which is deemed as being in northern Europe by Inequality Briefing, Guyane, one of its overseas regions, has a GDP of 53 (PPS) in 2011.
The poster implies that the nine of the poorest areas in northern Europe are all in the UK, from west Wales (which is number 1) to East Yorkshire and North Lincolnshire (number 10). Again, this is not entirely accurate if you look at the geographical area that is northern Europe, but is accurate when looking at the countries it deems as being in northern Europe: East Yorkshire has a PPS of 80, bigger than the whole of Estonia, which has PPS of 69.
It is also important that no British regions feature in the 20 poorest regions overall in the European Union according to the Eurostat data: they are all in Bulgaria, Romania, Hungary and Poland.
This does not mean that there is not huge inequality in Britain and the poster is accurate to point out that inner London did have the highest GDP per capita expressed as PPS in 2011. According to figures from the Equality Trust, inequality costs Britain £39billion every year through its impact on health and crime rates.