The relic is being toured around by the Knights of St. Columba, Thames River Valley, Portsmouth Province and you may have an opportunity to view it. Here is the schedule for this 2014 pilgrimage. The tour ends with Mass at Tyburn Convent, close to Marble Arch on July 27th. I understand this is where this particular relic is normally kept. Visiting priests may arrange to say mass at the convent chapel. The nuns there are dedicated to "Eucharistic Adoration for the glory of God and prayer for the needs of the whole human family."
The Tyburn nuns are within a very short distance of spot of the Tyburn Gallows. Some 105 Catholic martyrs, including Campion, where executed here. It is said that over 50,000 people were executed on those gallows. The first person executed was in 1196 the last in 1783. Overall there were some 350 Catholic martyrs for the faith in England.