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You should get your green card first, then apply for a Re-entry Permit before you leave the US. This may entitle you to retain your permanent resident status while you are in the UK. You will have to renew this permit every two years.
If I understand your question correctly, the university did not comply with the Sevis regulations. Their failure to comply may very likely prevent you from transferring to your new school. I would expect that the university will do everything in their power to rectify the problem because their noncompliance with the Sevis regulations can prevent them from admitting F-1 students in the future. You should follow up with the foreign student advisor, but be patient because the immigration...