Only if the hourly wage in £ has not grown faster relative to the hourly wage in DM.

Big wage increases are no use if most of it is eaten up by inflation. Germany has pursued a policy of a hard currency with low inflation and low currency fluctuation in order to increase predictability necessary for industrial investment. In that context, even low wage increases will improve living standards more than high wage increase in soft currency high inflation economies.

"Uncompetitive," in this context, is simply another word for "overvalued currency."

1. With soft currencies, devaluation is an ongoing process. I.e., one devaluation hides the next devaluation. Domestic industry can sell by price and does not have to increase productivity and innovation. Therefore, industry loses competitiveness.
   
2. German industry has had to face regular increases in the value  its currency. It has become competitive by a) shifting from low-cost to high added value industries b) increasing productivity c) improving technological innovation. Therefore it has become competitive.
   

With the Eurozone, China and the US have been playing middle-man for what was effectively Germany competing with Greece and Spain.

As a percentage of total German exports, exports to the EZone have fallen from 47 to 37% in the last decade. That trend is likely to continue in the future. European markets will continue to loose importance.
But I agree that the Euro is too cheap for German industry. This will compromise German competitiveness in the future due to the mechanism I have explained under 1) and 2) above. Anyways, the Germans don't need the exorbitant trade surplus they have now. It's a disadvantage more than an advantage because it puts political pressure on them and they risk loosing much of their foreign held assets when the debt bubble bursts.
But there is no way of decreasing your competitiveness in relation to Spain while at the same time increasing your competitiveness to compete against China or Japan.